1339:
279:
291:
1071:
244:
307:
225:(meaning that the only possible orientation of the spins are either "up" or "down"), which interact antiferromagnetically, is a simple example for frustration. In the ground state, two of the spins can be antiparallel but the third one cannot. This leads to an increase of possible orientations (six in this case) of the spins in the ground state, enhancing fluctuations and thus suppressing magnetic ordering.
404:. Both chiral spin state and Z2 spin liquid state have long RVB bonds that connect the same sub-lattice. In chiral spin state, different bond configurations can have complex amplitudes, while in Z2 spin liquid state, different bond configurations only have real amplitudes. The RVB state on triangle lattice also realizes the Z2 spin liquid, where different bond configurations only have real amplitudes. The
25:
264:
fluctuations of the valence bonds must be allowed, leading to a ground state consisting of a superposition of many different partitionings of spins into valence bonds. If the partitionings are equally distributed (with the same quantum amplitude), there is no preference for any specific partitioning ("valence bond liquid"). This kind of ground state wavefunction was proposed by
133:
1284:
1099:, a spin-1/2 antiferromagnet on a triangular lattice, displayed diffuse scattering. This was attributed to spinons arising from a 2D RVB state. Later theoretical work challenged this picture, arguing that all experimental results were instead consequences of 1D spinons confined to individual chains.
314:
The valence bonds do not have to be formed by nearest neighbors only and their distributions may vary in different materials. Ground states with large contributions of long range valence bonds have more low-energy spin excitations, as those valence bonds are easier to break up. On breaking, they form
228:
A recent research work used this concept in analyzing brain networks and surprisingly indicated frustrated interactions in the brain corresponding to flexible neural interactions. This observation highlights the generalization of the frustration phenomenon and proposes its investigation in biological
4188:
Banerjee, A.; Bridges, C. A.; Yan, J.-Q.; Aczel, A. A.; Li, L.; Stone, M. B.; Granroth, G. E.; Lumsden, M. D.; Yiu, Y.; Knolle, J.; Bhattacharjee, S.; Kovrizhin, D. L.; Moessner, R.; Tennant, D. A.; Mandrus, D. G.; Nagler, S. E. (2016). "Proximate Kitaev quantum spin liquid behaviour in a honeycomb
1245:
Large (millimeter size) single crystals of herbertsmithite were grown and characterized in 2011. These enabled more precise measurements of possible spin liquid properties. In particular, momentum-resolved inelastic neutron scattering experiments showed a broad continuum of excitations. This was
395:
gauge field which may confine the spinons etc. So the equal-amplitude nearest-neighbour RVB state on square lattice is unstable and does not corresponds to a quantum spin phase. It may describe a critical phase transition point between two stable phases. A version of RVB state which is stable and
251:
To build a ground state without magnetic moment, valence bond states can be used, where two electron spins form a spin 0 singlet due to the antiferromagnetic interaction. If every spin in the system is bound like this, the state of the system as a whole has spin 0 too and is non-magnetic. The two
365:
The first discussion of the RVB state on square lattice using the RVB picture only consider nearest neighbour bonds that connect different sub-lattices. The constructed RVB state is an equal amplitude superposition of all the nearest-neighbour bond configurations. Such a RVB state is believed to
263:
There are two things that still distinguish a VBS from a spin liquid: First, by ordering the bonds in a certain way, the lattice symmetry is usually broken, which is not the case for a spin liquid. Second, this ground state lacks long-range entanglement. To achieve this, quantum mechanical
180:
spin state, much in the way liquid water is in a disordered state compared to crystalline ice. However, unlike other disordered states, a quantum spin liquid state preserves its disorder to very low temperatures. A more modern characterization of quantum spin liquids involves their
136:
135:
140:
139:
134:
1187:
copper spins within a single layer, whereas coupling between layers is negligible. Therefore, it is a good realization of the antiferromagnetic spin-1/2 Heisenberg model on the kagome lattice, which is a prototypical theoretical example of a quantum spin liquid.
141:
1191:
Synthetic, polycrystalline herbertsmithite powder was first reported in 2005, and initial magnetic susceptibility studies showed no signs of magnetic order down to 2K. In a subsequent study, the absence of magnetic order was verified down to 50 mK,
1690:, etc. The data collected for very different strongly correlated Fermi systems demonstrate universal scaling behavior; in other words distinct materials with strongly correlated fermions unexpectedly turn out to be uniform, thus forming a new
1114:) by Kanoda's group in 2003. It may correspond to a gapless spin liquid with spinon Fermi surface (the so-called uniform RVB state). The peculiar phase diagram of this organic quantum spin liquid compound was first thoroughly mapped using
138:
1414:, collaborating with physicists from the University of Cambridge, and the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, measured the first signatures of these fractional particles, known as
3514:
Han, Tian-Heng; Helton, Joel S; Chu, Shaoyan; Nocera, Daniel G; Rodriguez-Rivera, Jose A; Broholm, Collin; Lee, Young S (2012). "Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet".
3637:
Han, Tian-Heng; Norman, MR; Wen, J-J; Rodriguez-Rivera, Jose A; Helton, Joel S; Broholm, Collin; Lee, Young S (2016). "Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite".
1657:
etc. Therefore, to agree/explain with the numerous experimental facts, extended quasiparticles paradigm based on FCQPT has to be introduced. The main point here is that the well-defined quasiparticles determine the
420:
Since there is no single experimental feature which identifies a material as a spin liquid, several experiments have to be conducted to gain information on different properties which characterize a spin liquid.
3309:
de Vries, M. A.; Stewart, J. R.; Deen, P. P.; Piatek, J. O.; Nilsen, G. J.; Ronnow, H. M.; Harrison, A. (2009). "Scale-free antiferromagnetic fluctuations in the S=1/2 kagome antiferromagnet herbertsmithite".
1196:
measurements revealed a broad spectrum of low energy spin excitations, and low-temperature specific heat measurements had power law scaling. This gave compelling evidence for a spin liquid state with gapless
120:
with their nearest neighbors, i.e. neighboring spins seek to be aligned in opposite directions. Quantum spin liquids generated further interest when in 1987 Anderson proposed a theory that described
489:
1545:
In
December 2021, the first direct measurement of a quantum spin liquid of the toric code type was reported, it was achieved by two teams: one exploring ground state and anyonic excitations on a
646:
315:
two free spins. Other excitations rearrange the valence bonds, leading to low-energy excitations even for short-range bonds. Something very special about spin liquids is that they support
210:
1239:
137:
396:
contains deconfined spinons is the chiral spin state. Later, another version of stable RVB state with deconfined spinons, the Z2 spin liquid, is proposed, which realizes the simplest
821:
739:
521:
2622:
Matan, K.; Ono, T.; Fukumoto, Y.; Sato, T. J.; et al. (2010). "Pinwheel valence-bond solid and triplet excitations in the two-dimensional deformed kagome lattice".
221:
if there exist competing exchange interactions that can not all be satisfied at the same time, leading to a large degeneracy of the system's ground state. A triangle of
713:
765:
581:
2771:
169:, stripes, or checkerboards. These long-range patterns are referred to as "magnetic order," and are analogous to the regular crystal structure formed by many solids.
157:. This highly disordered phase is the generic state of magnets at high temperatures, where thermal fluctuations dominate. Upon cooling, the spins will often enter a
1645:
paradigm based on the assumption that the effective mass is approximately constant, in the FCQPT theory the effective mass of new quasiparticles strongly depends on
1229:
1185:
548:
355:
1423:
393:
674:
4526:
Semeghini, G.; Levine, H.; Keesling, A.; Ebadi, S.; Wang, T. T.; Bluvstein, D.; Verresen, R.; Pichler, H.; Kalinowski, M.; Samajdar, R.; Omran, A. (2021-12-03).
1261:
and the low energy dynamic susceptibility, with the low temperature heat capacity strongly depending on magnetic field. This scaling is seen in certain quantum
1250:
and high-resolution, low-energy neutron scattering) refined this picture and determined there was actually a small spinon excitation gap of 0.07–0.09 meV.
409:
401:
2140:
Kivelson, Steven A.; Rokhsar, Daniel S.; Sethna, James P. (1987). "Topology of the resonating valence-bond state: Solitons and high-Tc superconductivity".
2587:
Nytko, Emily A.; Helton, Joel S.; Müller, Peter; Nocera, Daniel G. (2008). "A Structurally
Perfect S = 1/2 Metal−Organic Hybrid Kagome Antiferromagnet".
1242:, reinforced the identification of herbertsmithite as a gapless spin liquid material, although the exact characterization remained unclear as of 2010.
357:. In spin liquids, a spinon is created if one spin is not paired in a valence bond. It can move by rearranging nearby valence bonds at low energy cost.
4154:
Ying Ran, Michael
Hermele, Patrick A. Lee, Xiao-Gang Wen, (2006), "Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice",
43:
4404:
Satzinger, K. J.; Liu, Y.-J; Smith, A.; Knapp, C.; Newman, M.; Jones, C.; Chen, Z.; Quintana, C.; Mi, X.; Dunsworth, A.; Gidney, C. (2021-12-03).
3236:
Olariu, A; et al. (2008). "O NMR Study of the
Intrinsic Magnetic Susceptibility and Spin Dynamics of the Quantum Kagome Antiferromagnet ZnCu
2678:
Y. Shimizu; K. Miyagawa; K. Kanoda; M. Maesato; et al. (2003). "Spin Liquid State in an
Organic Mott Insulator with a Triangular Lattice".
272:(RVB) state. These states are of great theoretical interest as they are proposed to play a key role in high-temperature superconductor physics.
1993:
2971:
Pratt, F. L.; Baker, P. J.; Blundell, S. J.; Lancaster, T.; et al. (2011). "Magnetic and non-magnetic phases of a quantum spin liquid".
895:
278:
3797:
Helton, J. S.; et al. (2010). "Dynamic
Scaling in the Susceptibility of the Spin-1/2 Kagome Lattice Antiferromagnet Herbertsmithite".
3576:
Fu, Mingxuan; Imai, Takashi; Lee, Young S (2015). "Evidence for a gapped spin-liquid ground state in a kagome
Heisenberg antiferromagnet".
2856:
Coldea, R.; Tennant, D.A.; Tsvelik, A.M.; Tylczynski, Z. (12 Feb 2001). "Experimental realization of a 2D fractional quantum spin liquid".
1725:
Materials supporting quantum spin liquid states may have applications in data storage and memory. In particular, it is possible to realize
1338:
443:
2108:
3993:
Pozo, Guillermo; de la Presa, Patricia; Prato, Rafael; Morales, Irene; Marin, Pilar; Fransaer, Jan; Dominguez-Benetton, Xochitl (2020).
172:
Quantum spin liquids offer a dramatic alternative to this typical behavior. One intuitive description of this state is as a "liquid" of
767:
is therefore a good indication of a possible spin liquid phase. Some frustrated materials with different lattice structures and their
589:
3126:
Shores, Matthew P; Nytko, Emily A; Bartlett, Bart M; Nocera, Daniel G (2005). "A Structurally
Perfect S=1/2 Kagome Antigerromagnet".
2918:
Kohno, Masanori; Starkh, Oleg A; Balents, Leon (2007). "Spinons and triplons in spatially anisotropic frustrated antiferromagnets".
2051:
4380:
4309:
256:, while not being entangled with the other spins. If all spins are distributed to certain localized static bonds, this is called a
1422:. Their experimental results successfully matched with one of the main theoretical models for a quantum spin liquid, known as a
3065:
Yan, Simeng; Huse, David A; White, Steven R (2011). "Spin-liquid ground state of the S=1/2 kagome
Heisenberg antiferromagnet".
1442:) is a specific realization of a possible quantum spin liquid (QSL) representing a new type of strongly correlated electrical
4618:
3713:
1013:
experiments. If there is a local magnetic field present, the nuclear or muon spin would be affected which can be measured. H-
1607:
1580:
1277:
2081:
1370:(B) shifts to higher T reaching 15 K at B=14 Tesla. Observing that χ~C/T~M*, one concludes that the specific heat of YbRh
1730:
1714:
1066:, which couple via emergent gauge fields to the electromagnetic field, giving rise to a power-law optical conductivity.
121:
4696:
3444:
Han, TH; Helton, JS; Chu, S; Prodi, Andrea; Singh, DK; Mazzoli, Claudio; Müller, P; Nocera, DG; Lee, Young S (2011).
1946:
61:
1410:
Another evidence of quantum spin liquid was observed in a 2-dimensional material in August 2015. The researchers of
3928:
Shaginyan, V. R.; Amusia, M. Ya.; Msezane, A. Z.; Popov, K. G. (2010). "Scaling
Behavior of Heavy Fermion Metals".
3860:
de Vries, M. A.; et al. (2008). "The magnetic ground state of an experimental S=1/2 kagomé antiferromagnet".
1726:
290:
1288:
1029:
have shown no sign of magnetic ordering down to 32 mK, which is four orders of magnitude smaller than the
238:
4253:
Shaginyan, V. R.; et al. (2012). "Identification of Strongly Correlated Spin Liquid in Herbertsmithite".
1129:
is one of the most extensively studied QSL candidate materials. It is a mineral with chemical composition ZnCu
165:) phase. In this phase, interactions between the spins cause them to align into large-scale patterns, such as
4681:
1963:
1537:, which does not develop long-range order even below 1 K, and has a diffuse spectrum of gapless excitations.
1411:
1729:
by means of spin-liquid states. Developments in quantum spin liquids may also help in the understanding of
1493:, contrary to conventional insulators. There are a few candidates of SCI; the most promising among them is
1193:
173:
90:
in certain magnetic materials. Quantum spin liquids (QSL) are generally characterized by their long-range
1314:
shifts to higher T reaching 14 K at B=18 Tesla. Observing that C/T~χ~M*, one concludes that SCQSL in ZnCu
1145:
crystal structure. Notably, the copper ions within this structure form stacked two-dimensional layers of
2369:
Moessner, R.; Sondhi, S. L. (2002). "Resonating Valence Bond Liquid Physics on the Triangular Lattice".
1030:
201:
Several physical models have a disordered ground state that can be described as a quantum spin liquid.
2783:
T. Ng & P. A. Lee (2007). "Power-Law Conductivity inside the Mott Gap: Application to κ-(BEDT-TTF)
4691:
3446:"Synthesis and characterization of single crystals of the spin-1/2 kagome-lattice antiferromagnets Zn
3161:
Helton, J. S.; et al. (2007). "Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu
1040:
give information about the low-energy density of states, which can be compared to theoretical models.
253:
4088:
Shaginyan, V. R.; Msezane, A.; Popov, K. (2011). "Thermodynamic Properties of Kagome Lattice in ZnCu
3962:
4167:
2252:
1846:
1667:
1591:
75:
4651:
785:
718:
496:
493:
Fitting experimental data to this equation determines a phenomenological Curie–Weiss temperature,
4701:
3862:
3799:
3175:
1560:
1443:
1258:
434:
218:
319:, meaning excitations with fractional quantum numbers. A prominent example is the excitation of
4048:
3957:
3445:
2247:
1566:
1266:
1254:
1115:
679:
2283:
Read, N.; Sachdev, Subir (1991). "Large-N expansion for frustrated quantum antiferromagnets".
744:
557:
247:
Valence bond solid. The bonds form a specific pattern and consist of pairs of entangled spins.
2741:
2506:
1246:
interpreted as evidence for gapless, fractionalized spinons. Follow-up experiments (using O
39:
4549:
4492:
4427:
4331:
4274:
4208:
4121:
4057:
3949:
3881:
3818:
3752:
3657:
3595:
3534:
3486:
3410:
3329:
3267:
3194:
3084:
3031:
2980:
2937:
2875:
2814:
2697:
2641:
2494:
2441:
2388:
2335:
2292:
2239:
2196:
2149:
2005:
1891:
1771:
1663:
1362:
at B=7 Tesla are shown. T-dependence T at B=0 is depicted by the solid curve. The maximum χ
1257:
behavior. Magnetic response of this material displays scaling relation in both the bulk ac
1200:
1156:
526:
326:
186:
91:
2326:
Wen, Xiao-Gang (1991). "Mean Field Theory of Spin Liquid States with Finite Energy Gaps".
1342:
Fig.2: T-dependence of the magnetic susceptibility χ at different magnetic fields for ZnCu
369:
8:
2230:
Wen, Xiao-Gang; Wilczek, F.; Zee, A. (1989). "Chiral Spin States and Superconductivity".
1033:
J≈250 K between neighboring spins in this compound. Further investigations include:
653:
438:
4553:
4496:
4431:
4335:
4278:
4212:
4125:
4061:
3953:
3885:
3822:
3756:
3729:
Wen, Jinsheng; Yu, Shun-Li; Li, Shiyan; Yu, Weiqiang; Li, Jian-Xin (12 September 2019).
3661:
3636:
3599:
3538:
3513:
3490:
3414:
3333:
3271:
3198:
3088:
3035:
2984:
2941:
2879:
2818:
2701:
2645:
2498:
2445:
2392:
2339:
2296:
2243:
2200:
2153:
2009:
1895:
1783:
1775:
1549:
and the other implementing a theoretical blueprint of atoms on a ruby lattice held with
4573:
4539:
4508:
4482:
4451:
4417:
4355:
4321:
4290:
4264:
4232:
4198:
4137:
4111:
3975:
3939:
3905:
3871:
3842:
3808:
3776:
3742:
3673:
3647:
3619:
3585:
3558:
3524:
3476:
3426:
3400:
3361:
3319:
3291:
3257:
3218:
3184:
3108:
3074:
3004:
2953:
2927:
2899:
2865:
2838:
2804:
2721:
2687:
2657:
2631:
2560:
2542:
2510:
2484:
2457:
2431:
2404:
2378:
2029:
1915:
1795:
1761:
117:
113:
102:
4527:
4470:
4405:
2453:
153:, where each individual spin behaves independently of the rest, just like atoms in an
4577:
4565:
4512:
4455:
4443:
4359:
4347:
4294:
4224:
4141:
4102:
4016:
3979:
3909:
3897:
3834:
3780:
3768:
3709:
3677:
3611:
3550:
3430:
3353:
3345:
3283:
3210:
3143:
3100:
3047:
2996:
2891:
2830:
2713:
2661:
2604:
2564:
2461:
2422:
Kitaev, A.Yu.; Balents, Leon (2003). "Fault-tolerant quantum computation by anyons".
2408:
2351:
2308:
2265:
2212:
2165:
2047:
2021:
1942:
1935:
1907:
1831:
1787:
1710:
1554:
1546:
768:
397:
182:
95:
4070:
4035:
3846:
3623:
3222:
3112:
2957:
2903:
2842:
2514:
1919:
1799:
4686:
4557:
4500:
4435:
4339:
4286:
4282:
4236:
4216:
4129:
4065:
4006:
3967:
3893:
3889:
3830:
3826:
3760:
3730:
3701:
3665:
3603:
3562:
3542:
3494:
3418:
3365:
3341:
3337:
3295:
3279:
3275:
3202:
3135:
3092:
3039:
3008:
2988:
2945:
2883:
2822:
2725:
2705:
2649:
2596:
2552:
2533:
Norman, M.R. (2016). "Herbertsmithite and the Search for the Quantum Spin Liquid".
2502:
2449:
2396:
2343:
2300:
2257:
2204:
2157:
2120:
2033:
2013:
1899:
1827:
1779:
1550:
1415:
1262:
676:. An ideal quantum spin liquid would not develop magnetic order at any temperature
551:
109:
83:
4625:
3971:
3206:
2826:
2709:
1903:
1269:, and two-dimensional He as a signature of proximity to a quantum critical point.
4652:"New kind of magnetism discovered: Experiments demonstrate 'quantum spin liquid'"
3930:
2556:
2086:
2056:
1703:
1691:
1570:
1494:
1451:
1153:
over the oxygen bonds creates a strong antiferromagnetic interaction between the
1126:
1074:
862:
166:
162:
3695:
3043:
2887:
2304:
2208:
771:
are listed in the table below. All of them are proposed spin liquid candidates.
4593:"This Weird Crystal Demonstrates a New Magnetic Behavior That Works Like Magic"
4504:
4133:
3698:
Theory of Heavy-Fermion Compounds - Theory of Strongly Correlated Fermi-Systems
3669:
3499:
2185:"Equivalence of the resonating-valence-bond and fractional quantum Hall states"
1628:
1621:
1595:
1483:
1146:
977:
953:
901:
868:
265:
87:
3764:
3705:
3379:
Mendels, Philippe; Bert, Fabrice (2010). "Quantum kagome antiferromagnet: ZnCu
2475:
Knolle, Johannes; Moessner, Roderich (2019). "A field guide to spin liquids".
2261:
1561:
Specific properties: topological fermion condensation quantum phase transition
4675:
4255:
3772:
3349:
2347:
2161:
2077:
1818:
P. W. Anderson (1973). "Resonating valence bonds: A new kind of insulator?".
1699:
1674:
properties of strongly correlated Fermi systems and M* becomes a function of
1659:
1577:
1475:
1459:
1447:
1276:
of herbertsmithite (~10 nm) were synthesized at room temperature, using
1273:
1150:
412:) that explicitly breaks the spin rotation symmetry and is exactly solvable.
177:
98:
4561:
4439:
4343:
3607:
3096:
3022:
Elser, Veit (1989). "Nuclear antiferromagnetism in a registered 3He solid".
1606:. The emergence of FCQPT is directly related to the unlimited growth of the
1378:
shown in Fig. 1 exhibits the similar behavior as χ does. Thus, SCQSL in ZnCu
650:
In a classic antiferromagnet, the two temperatures should coincide and give
550:, where magnetic order in the material begins to develop, as evidenced by a
4592:
4569:
4447:
4351:
4228:
4020:
3901:
3838:
3615:
3554:
3422:
3357:
3287:
3214:
3147:
3104:
3051:
3000:
2895:
2834:
2717:
2608:
2312:
2216:
2025:
1911:
1791:
1534:
1280:, showing that their spin liquid nature persists at such small dimensions.
1142:
2355:
2269:
2169:
1070:
4155:
3189:
2870:
2738:
In literature, the value of J is commonly given in units of temperature (
2692:
2436:
2383:
2125:
1614:
1603:
1599:
1587:
1052:
gives information about the nature of excitations and correlations (e.g.
158:
3546:
2992:
2677:
2400:
2100:
2017:
1298:
at different magnetic fields as shown in the legend. The values of (C/T)
209:
4011:
3994:
3064:
2107:
Saberi M, Khosrowabadi R, Khatibi A, Misic B, Jafari G (October 2022).
1326:
shown in Fig. 2 exhibits the similar behavior as heavy fermions in YbRh
430:
405:
222:
150:
4528:"Probing topological spin liquids on a programmable quantum simulator"
3139:
2653:
2600:
1102:
Afterwards, it was observed in an organic Mott insulator (κ-(BEDT-TTF)
1005:
One of the most direct evidence for absence of magnetic ordering give
4469:
Verresen, Ruben; Lukin, Mikhail D.; Vishwanath, Ashvin (2021-07-08).
4220:
2949:
1671:
243:
154:
3700:. Springer Series in Solid-State Sciences. Vol. 182. Springer.
3443:
2184:
4544:
4487:
4422:
4326:
4203:
3747:
3652:
3590:
2547:
2489:
1766:
1706:
1635:
1573:
1419:
1234:
excitations. A broad array of additional experiments, including O
4471:"Prediction of Toric Code Topological Order from Rydberg Blockade"
4269:
4116:
3944:
3876:
3813:
3529:
3481:
3405:
3324:
3262:
3079:
2932:
2809:
2636:
2109:"Pattern of frustration formation in the functional brain network"
1752:
Savary, L.; Balents, L. (2017). "Quantum spin liquids: a review".
1474:=3, as it should be in the case of a conventional insulator whose
1498:
1077:, the mineral whose ground state was shown to have QSL behaviour
306:
4406:"Realizing topologically ordered states on a quantum processor"
4310:"Realizing topologically ordered states on a quantum processor"
3696:
Amusia, M.; Popov, K.; Shaginyan, V.; Stephanovich, V. (2014).
1874:
P. W. Anderson (1987). "The resonating valence bond state in La
1642:
1231:
1063:
1053:
320:
2855:
2106:
1010:
108:
The quantum spin liquid state was first proposed by physicist
1695:
190:
4525:
4168:"New state of matter detected in a two-dimensional material"
1418:, in a two-dimensional material with a structure similar to
1287:
Fig. 1: T-dependence of the electronic specific heat C/T of
268:
in 1973 as the ground state of spin liquids and is called a
3992:
3927:
2970:
145:
Example of a spin liquid emerging from frustrated magnetism
2052:"Physicists Aim to Classify All Possible Phases of Matter"
1429:
1091:
Neutron scattering measurements of cesium chlorocuprate Cs
4619:"Topological Quantum Computation from non-abelian anyons"
4381:"Quantum Simulators Create a Totally New Phase of Matter"
4036:"High-field phase diagram of the heavy-fermion metal YbRh
3308:
3125:
1247:
1235:
1014:
1006:
284:
One possible short-range pairing of spins in a RVB state.
1489:
is applied to SCI the specific heat depends strongly on
1283:
1046:
can determine if excitations are localized or itinerant.
408:
model is yet another realization of Z2 spin liquid (and
4468:
4187:
2586:
112:
in 1973 as the ground state for a system of spins on a
4403:
4160:
3995:"Spin transition nanoparticles made electrochemically"
360:
4087:
3731:"Experimental identification of quantum spin liquids"
2744:
2139:
1964:"A Strange New Quantum State of Matter: Spin Liquids"
1203:
1159:
788:
747:
721:
682:
656:
592:
560:
529:
499:
484:{\displaystyle \chi \sim {\frac {C}{T-\Theta _{CW}}}}
446:
415:
372:
329:
2621:
715:
and so would have a diverging frustration parameter
1747:
1745:
34:
may be too technical for most readers to understand
2917:
2765:
1934:
1450:metals with one exception: it resists the flow of
1223:
1179:
815:
759:
733:
707:
668:
640:
575:
542:
515:
483:
387:
349:
641:{\displaystyle f={\frac {|\Theta _{cw}|}{T_{c}}}}
232:
4673:
2182:
1742:
1366:(T) decreases as magnetic field B grows, while T
1310:decreases with growing magnetic field B, while T
1932:
2782:
2528:
2526:
2524:
2474:
2368:
2082:"Inside the Knotty World of 'Anyon' Particles"
1996:(2010). "Spin liquids in frustrated magnets".
1873:
1817:
204:
3691:
3689:
3687:
2421:
2229:
1751:
1462:of this type of insulator is proportional to
2908:Note that the preprint was uploaded in 2000.
2673:
2671:
2362:
2176:
2133:
1992:
1869:
1867:
1813:
1811:
1809:
124:in terms of a disordered spin-liquid state.
4610:
4248:
4246:
3378:
3372:
3302:
2521:
2282:
1988:
1986:
1984:
323:which are neutral in charge and carry spin
4643:
3684:
3229:
3154:
3119:
2849:
2468:
2415:
2371:Progress of Theoretical Physics Supplement
424:
4543:
4486:
4421:
4325:
4268:
4252:
4202:
4115:
4069:
4033:
4010:
3961:
3943:
3875:
3812:
3746:
3728:
3651:
3589:
3575:
3528:
3498:
3480:
3404:
3323:
3261:
3188:
3078:
3015:
2964:
2931:
2911:
2869:
2808:
2691:
2668:
2635:
2615:
2580:
2546:
2488:
2477:Annual Review of Condensed Matter Physics
2435:
2382:
2251:
2124:
2070:
2046:
2040:
1933:Chaikin, Paul M; Lubensky, Tom C (1995).
1864:
1838:
1806:
1765:
1402:It may realize a U(1)-Dirac spin liquid.
1306:at B=8 Tesla are shown. The maximum (C/T)
149:The simplest kind of magnetic phase is a
62:Learn how and when to remove this message
46:, without removing the technical details.
4649:
4624:. University of Virginia. Archived from
4243:
4181:
3986:
3859:
3792:
3790:
3393:Journal of the Physical Society of Japan
3128:Journal of the American Chemical Society
2589:Journal of the American Chemical Society
2507:10.1146/annurev-conmatphys-031218-013401
2276:
1981:
1337:
1282:
1069:
305:
242:
208:
131:
4590:
4584:
4148:
4083:
4081:
3853:
3630:
3507:
3437:
3058:
2319:
2223:
2076:
1961:
1844:
1613:*. Near FCQPT, M* starts to depend on
1436:strongly correlated quantum spin liquid
1430:Strongly correlated quantum spin liquid
4674:
4156:https://arxiv.org/abs/cond-mat/0611414
3796:
3569:
3235:
3160:
2532:
2183:Kalmeyer, V.; Laughlin, R. B. (1987).
1937:Principles of Condensed-Matter Physics
1634:and other external parameters such as
1405:
1081:
4650:Chandler, David (December 20, 2012).
3923:
3921:
3919:
3787:
3021:
1962:Wilkins, Alasdair (August 15, 2011).
1272:In 2020, monodisperse single-crystal
1253:Some measurements were suggestive of
44:make it understandable to non-experts
4591:Aguilar, Mario (December 20, 2012).
4378:
4307:
4078:
4027:
2776:
1565:The experimental facts collected on
1278:gas-diffusion electrocrystallization
213:Frustrated Ising spins on a triangle
18:
4616:
4034:Gegenwart, P.; et al. (2006).
2577:Phys. Rev. Lett. 116, 107203 (2016)
2325:
1926:
1586:* is very large, or even diverges.
1446:(SCI) that possesses properties of
583:. The ratio of these is called the
361:Realizations of (stable) RVB states
127:
101:, and absence of ordinary magnetic
13:
3916:
1955:
1847:"A new spin on superconductivity?"
1731:high temperature superconductivity
1715:high-temperature superconductivity
1540:
1238:, and neutron spectroscopy of the
1121:
806:
790:
728:
608:
523:. There is a second temperature,
501:
466:
416:Experimental signatures and probes
122:high-temperature superconductivity
86:that can be formed by interacting
14:
4713:
1390:behaves as heavy fermions in YbRh
1240:dynamic magnetic structure factor
429:In a high-temperature, classical
1845:Trafton, Anne (March 28, 2011).
289:
277:
23:
4519:
4462:
4397:
4372:
4301:
3722:
2732:
2571:
1727:topological quantum computation
1720:
3894:10.1103/PhysRevLett.100.157205
3831:10.1103/PhysRevLett.104.147201
3342:10.1103/PhysRevLett.103.237201
3280:10.1103/PhysRevLett.100.087202
1941:. Cambridge university press.
1754:Reports on Progress in Physics
1516:
1044:Thermal transport measurements
810:
802:
725:
702:
683:
621:
603:
570:
564:
382:
376:
301:
239:Resonating valence bond theory
233:Resonating valence bonds (RVB)
1:
3972:10.1016/j.physrep.2010.03.001
3207:10.1103/PhysRevLett.98.107204
2827:10.1103/PhysRevLett.99.156402
2710:10.1103/PhysRevLett.91.107001
2454:10.1016/S0003-4916(02)00018-0
1904:10.1126/science.235.4793.1196
1784:10.1088/0034-4885/80/1/016502
1736:
1412:Oak Ridge National Laboratory
950:Cu-(1,3-benzenedicarboxylate)
310:Spinon moving in spin liquids
4379:Wood, Charlie (2021-12-02).
4308:Wood, Charlie (2021-12-02).
2557:10.1103/RevModPhys.88.041002
1832:10.1016/0025-5408(73)90167-0
1501:with chemical structure ZnCu
1470:less or equal 1 rather than
1194:inelastic neutron scattering
1017:measurements on κ-(BEDT-TTF)
816:{\displaystyle \Theta _{cw}}
734:{\displaystyle f\to \infty }
516:{\displaystyle \Theta _{CW}}
296:Long-range pairing of spins.
7:
3044:10.1103/PhysRevLett.62.2405
2888:10.1103/PhysRevLett.86.1335
2305:10.1103/physrevlett.66.1773
2209:10.1103/physrevlett.59.2095
1820:Materials Research Bulletin
1086:
252:spins forming the bond are
205:Frustrated magnetic moments
196:
10:
4718:
4505:10.1103/PhysRevX.11.031005
4287:10.1209/0295-5075/97/56001
4134:10.1103/PhysRevB.84.060401
3670:10.1103/PhysRevB.94.060409
3500:10.1103/PhysRevB.83.100402
1641:, etc. In contrast to the
1038:Specific heat measurements
236:
176:spins, in comparison to a
4071:10.1088/1367-2630/8/9/171
3765:10.1038/s41535-019-0151-6
3706:10.1007/978-3-319-10825-4
2535:Reviews of Modern Physics
2262:10.1103/physrevb.39.11413
1567:heavy fermion (HF) metals
708:{\displaystyle (T_{c}=0)}
366:contain emergent gapless
4697:Condensed matter physics
2348:10.1103/physrevb.44.2664
2162:10.1103/physrevb.35.8865
1882:and superconductivity".
1592:quantum phase transition
1060:Reflectance measurements
1000:
760:{\displaystyle f>100}
576:{\displaystyle \chi (T)}
76:condensed matter physics
4562:10.1126/science.abi8794
4440:10.1126/science.abi8378
4344:10.1126/science.abi8378
3863:Physical Review Letters
3800:Physical Review Letters
3608:10.1126/science.aab2120
3312:Physical Review Letters
3250:Physical Review Letters
3176:Physical Review Letters
3097:10.1126/science.1201080
3024:Physical Review Letters
2858:Physical Review Letters
2797:Physical Review Letters
2766:{\displaystyle J/k_{B}}
2680:Physical Review Letters
2285:Physical Review Letters
2189:Physical Review Letters
1702:, quantum spin liquid,
769:Curie–Weiss temperature
435:magnetic susceptibility
425:Magnetic susceptibility
270:resonating valence bond
4049:New Journal of Physics
3423:10.1143/JPSJ.79.011001
2767:
1454:. At low temperatures
1424:Kitaev honeycomb model
1399:
1335:
1225:
1181:
1116:muon spin spectroscopy
1078:
841:anisotropic triangular
817:
761:
735:
709:
670:
642:
577:
544:
517:
485:
389:
351:
311:
248:
214:
146:
3735:npj Quantum Materials
2768:
1590:fermion condensation
1576:demonstrate that the
1535:kagome bilayer magnet
1341:
1286:
1226:
1224:{\displaystyle S=1/2}
1182:
1180:{\displaystyle S=1/2}
1073:
818:
762:
736:
710:
671:
643:
585:frustration parameter
578:
545:
543:{\displaystyle T_{c}}
518:
486:
390:
352:
350:{\displaystyle S=1/2}
309:
246:
212:
144:
118:antiferromagnetically
4682:Correlated electrons
2773:) instead of energy.
2742:
2126:10.1162/netn_a_00268
2113:Network Neuroscience
1694:that consists of HF
1267:heavy-fermion metals
1201:
1157:
786:
745:
719:
680:
654:
590:
558:
527:
497:
444:
410:Z2 topological order
402:Z2 topological order
388:{\displaystyle U(1)}
370:
327:
217:Localized spins are
187:quantum entanglement
92:quantum entanglement
4554:2021Sci...374.1242S
4538:(6572): 1242–1247.
4497:2021PhRvX..11c1005V
4432:2021Sci...374.1237S
4416:(6572): 1237–1241.
4336:2021Sci...374.1237S
4320:(6572): 1237–1241.
4279:2012EL.....9756001S
4213:2016NatMa..15..733B
4126:2011PhRvB..84f0401S
4062:2006NJPh....8..171G
3954:2010PhR...492...31S
3886:2008PhRvL.100o7205D
3823:2010PhRvL.104n7201H
3757:2019npjQM...4...12W
3662:2016PhRvB..94f0409H
3600:2015Sci...350..655F
3547:10.1038/nature11659
3539:2012Natur.492..406H
3491:2011PhRvB..83j0402H
3415:2010JPSJ...79a1001M
3334:2009PhRvL.103w7201D
3272:2008PhRvL.100h7202O
3199:2007PhRvL..98j7204H
3134:(39): 13462–13463.
3089:2011Sci...332.1173Y
3073:(6034): 1173–1176.
3036:1989PhRvL..62.2405E
2993:10.1038/nature09910
2985:2011Natur.471..612P
2942:2007NatPh...3..790K
2880:2001PhRvL..86.1335C
2819:2007PhRvL..99o6402N
2702:2003PhRvL..91j7001S
2646:2010NatPh...6..865M
2499:2019ARCMP..10..451K
2446:2003AnPhy.303....2K
2401:10.1143/PTPS.145.37
2393:2002PThPS.145...37M
2340:1991PhRvB..44.2664W
2297:1991PhRvL..66.1773R
2244:1989PhRvB..3911413W
2238:(16): 11413–11423.
2201:1987PhRvL..59.2095K
2154:1987PhRvB..35.8865K
2018:10.1038/nature08917
2010:2010Natur.464..199B
1896:1987Sci...235.1196A
1890:(4793): 1196–1198.
1776:2017RPPh...80a6502S
1478:is proportional to
1406:Kitaev spin liquids
1082:Candidate materials
669:{\displaystyle f=1}
254:maximally entangled
80:quantum spin liquid
4100:Herbertsmithite".
4012:10.1039/C9NR09884D
2763:
2048:Wolchover, Natalie
1594:(FCQPT) preserves
1400:
1336:
1221:
1177:
1079:
1050:Neutron scattering
813:
757:
731:
705:
666:
638:
573:
540:
513:
481:
385:
347:
317:exotic excitations
312:
258:valence bond solid
249:
215:
147:
114:triangular lattice
4475:Physical Review X
4103:Physical Review B
3715:978-3-319-10825-4
3640:Physical Review B
3584:(6261): 655–658.
3523:(7429): 406–410.
3469:Physical Review B
3140:10.1021/ja053891p
3030:(20): 2405–2408.
2979:(7340): 612–616.
2654:10.1038/nphys1761
2601:10.1021/ja709991u
2595:(10): 2922–2923.
2424:Annals of Physics
2328:Physical Review B
2291:(13): 1773–1776.
2232:Physical Review B
2195:(18): 2095–2098.
2148:(16): 8865–8868.
2142:Physical Review B
2004:(7286): 199–208.
1598:, and forms flat
1555:quantum simulator
1547:quantum processor
1416:Majorana fermions
1354:. The values of χ
1031:coupling constant
998:
997:
636:
479:
398:topological order
183:topological order
142:
72:
71:
64:
4709:
4692:Phases of matter
4667:
4666:
4664:
4662:
4647:
4641:
4640:
4638:
4636:
4630:
4623:
4614:
4608:
4607:
4605:
4603:
4588:
4582:
4581:
4547:
4523:
4517:
4516:
4490:
4466:
4460:
4459:
4425:
4401:
4395:
4394:
4392:
4391:
4376:
4370:
4369:
4367:
4366:
4329:
4305:
4299:
4298:
4272:
4250:
4241:
4240:
4221:10.1038/nmat4604
4206:
4191:Nature Materials
4185:
4179:
4178:
4176:
4174:
4164:
4158:
4152:
4146:
4145:
4119:
4085:
4076:
4075:
4073:
4031:
4025:
4024:
4014:
4005:(9): 5412–5421.
3990:
3984:
3983:
3965:
3947:
3925:
3914:
3913:
3879:
3857:
3851:
3850:
3816:
3794:
3785:
3784:
3750:
3726:
3720:
3719:
3693:
3682:
3681:
3655:
3634:
3628:
3627:
3593:
3573:
3567:
3566:
3532:
3511:
3505:
3504:
3502:
3484:
3466:
3441:
3435:
3434:
3408:
3376:
3370:
3369:
3327:
3306:
3300:
3299:
3265:
3233:
3227:
3226:
3192:
3190:cond-mat/0610539
3158:
3152:
3151:
3123:
3117:
3116:
3082:
3062:
3056:
3055:
3019:
3013:
3012:
2968:
2962:
2961:
2950:10.1038/nphys749
2935:
2915:
2909:
2907:
2873:
2871:cond-mat/0007172
2864:(7): 1335–1338.
2853:
2847:
2846:
2812:
2780:
2774:
2772:
2770:
2769:
2764:
2762:
2761:
2752:
2736:
2730:
2729:
2695:
2693:cond-mat/0307483
2675:
2666:
2665:
2639:
2619:
2613:
2612:
2584:
2578:
2575:
2569:
2568:
2550:
2530:
2519:
2518:
2492:
2472:
2466:
2465:
2439:
2437:quant-ph/9707021
2419:
2413:
2412:
2386:
2384:cond-mat/0205029
2366:
2360:
2359:
2334:(6): 2664–2672.
2323:
2317:
2316:
2280:
2274:
2273:
2255:
2227:
2221:
2220:
2180:
2174:
2173:
2137:
2131:
2130:
2128:
2119:(4): 1334–1356.
2104:
2098:
2097:
2095:
2094:
2074:
2068:
2067:
2065:
2064:
2044:
2038:
2037:
1990:
1979:
1978:
1976:
1974:
1959:
1953:
1952:
1940:
1930:
1924:
1923:
1871:
1862:
1861:
1859:
1857:
1842:
1836:
1835:
1815:
1804:
1803:
1769:
1749:
1551:optical tweezers
1533:is a frustrated
1263:antiferromagnets
1255:quantum critical
1230:
1228:
1227:
1222:
1217:
1186:
1184:
1183:
1178:
1173:
1149:. Additionally,
822:
820:
819:
814:
809:
801:
800:
774:
773:
766:
764:
763:
758:
741:. A large value
740:
738:
737:
732:
714:
712:
711:
706:
695:
694:
675:
673:
672:
667:
647:
645:
644:
639:
637:
635:
634:
625:
624:
619:
618:
606:
600:
582:
580:
579:
574:
549:
547:
546:
541:
539:
538:
522:
520:
519:
514:
512:
511:
490:
488:
487:
482:
480:
478:
477:
476:
454:
437:is given by the
394:
392:
391:
386:
356:
354:
353:
348:
343:
293:
281:
189:properties, and
143:
128:Basic properties
67:
60:
56:
53:
47:
27:
26:
19:
4717:
4716:
4712:
4711:
4710:
4708:
4707:
4706:
4672:
4671:
4670:
4660:
4658:
4648:
4644:
4634:
4632:
4628:
4621:
4617:Fendley, Paul.
4615:
4611:
4601:
4599:
4589:
4585:
4524:
4520:
4467:
4463:
4402:
4398:
4389:
4387:
4385:Quanta Magazine
4377:
4373:
4364:
4362:
4306:
4302:
4251:
4244:
4186:
4182:
4172:
4170:
4166:
4165:
4161:
4153:
4149:
4099:
4095:
4091:
4086:
4079:
4043:
4039:
4032:
4028:
3991:
3987:
3963:10.1.1.749.3376
3931:Physics Reports
3926:
3917:
3858:
3854:
3795:
3788:
3727:
3723:
3716:
3694:
3685:
3635:
3631:
3574:
3570:
3512:
3508:
3464:
3461:
3457:
3453:
3449:
3442:
3438:
3390:
3386:
3382:
3377:
3373:
3307:
3303:
3247:
3243:
3239:
3234:
3230:
3172:
3168:
3164:
3159:
3155:
3124:
3120:
3063:
3059:
3020:
3016:
2969:
2965:
2916:
2912:
2854:
2850:
2794:
2790:
2786:
2781:
2777:
2757:
2753:
2748:
2743:
2740:
2739:
2737:
2733:
2676:
2669:
2630:(11): 865–869.
2620:
2616:
2585:
2581:
2576:
2572:
2531:
2522:
2473:
2469:
2420:
2416:
2367:
2363:
2324:
2320:
2281:
2277:
2228:
2224:
2181:
2177:
2138:
2134:
2105:
2101:
2092:
2090:
2087:Quanta Magazine
2075:
2071:
2062:
2060:
2057:Quanta Magazine
2045:
2041:
1991:
1982:
1972:
1970:
1960:
1956:
1949:
1931:
1927:
1881:
1877:
1872:
1865:
1855:
1853:
1843:
1839:
1816:
1807:
1750:
1743:
1739:
1723:
1704:two-dimensional
1692:state of matter
1571:two dimensional
1563:
1543:
1541:Toric code type
1532:
1528:
1524:
1519:
1512:
1508:
1504:
1495:Herbertsmithite
1452:electric charge
1432:
1408:
1397:
1393:
1389:
1385:
1381:
1377:
1373:
1369:
1365:
1361:
1357:
1353:
1349:
1345:
1333:
1329:
1325:
1321:
1317:
1313:
1309:
1305:
1301:
1296:
1292:
1213:
1202:
1199:
1198:
1169:
1158:
1155:
1154:
1147:kagome lattices
1140:
1136:
1132:
1127:Herbertsmithite
1124:
1122:Herbertsmithite
1113:
1109:
1105:
1098:
1094:
1089:
1084:
1075:Herbertsmithite
1028:
1024:
1020:
1003:
989:
974:
970:
966:
939:
935:
921:
917:
913:
893:
889:
885:
881:
863:herbertsmithite
860:
856:
852:
838:
834:
830:
805:
793:
789:
787:
784:
783:
746:
743:
742:
720:
717:
716:
690:
686:
681:
678:
677:
655:
652:
651:
630:
626:
620:
611:
607:
602:
601:
599:
591:
588:
587:
559:
556:
555:
534:
530:
528:
525:
524:
504:
500:
498:
495:
494:
469:
465:
458:
453:
445:
442:
441:
439:Curie–Weiss law
427:
418:
371:
368:
367:
363:
339:
328:
325:
324:
304:
297:
294:
285:
282:
241:
235:
207:
199:
163:antiferromagnet
132:
130:
84:phase of matter
68:
57:
51:
48:
40:help improve it
37:
28:
24:
17:
16:Phase of matter
12:
11:
5:
4715:
4705:
4704:
4702:Quasiparticles
4699:
4694:
4689:
4684:
4669:
4668:
4642:
4609:
4583:
4518:
4461:
4396:
4371:
4300:
4242:
4197:(7): 733–740.
4180:
4159:
4147:
4097:
4093:
4089:
4077:
4041:
4037:
4026:
3985:
3915:
3870:(15): 157205.
3852:
3807:(14): 147201.
3786:
3721:
3714:
3683:
3629:
3568:
3506:
3475:(10): 100402.
3459:
3455:
3451:
3447:
3436:
3388:
3384:
3380:
3371:
3318:(23): 237201.
3301:
3245:
3241:
3237:
3228:
3183:(10): 107204.
3170:
3166:
3162:
3153:
3118:
3057:
3014:
2963:
2920:Nature Physics
2910:
2848:
2803:(15): 156402.
2792:
2788:
2784:
2775:
2760:
2756:
2751:
2747:
2731:
2686:(10): 107001.
2667:
2624:Nature Physics
2614:
2579:
2570:
2520:
2467:
2414:
2361:
2318:
2275:
2253:10.1.1.676.519
2222:
2175:
2132:
2099:
2080:(2017-02-28).
2078:Wilczek, Frank
2069:
2050:(2018-01-03).
2039:
1980:
1954:
1947:
1925:
1879:
1875:
1863:
1837:
1826:(2): 153–160.
1805:
1740:
1738:
1735:
1722:
1719:
1629:magnetic field
1622:number density
1608:effective mass
1596:quasiparticles
1581:effective mass
1562:
1559:
1542:
1539:
1530:
1526:
1522:
1518:
1515:
1510:
1506:
1502:
1484:magnetic field
1431:
1428:
1407:
1404:
1395:
1391:
1387:
1383:
1379:
1375:
1371:
1367:
1363:
1359:
1355:
1351:
1347:
1343:
1331:
1327:
1323:
1319:
1315:
1311:
1307:
1303:
1299:
1294:
1290:
1259:susceptibility
1220:
1216:
1212:
1209:
1206:
1176:
1172:
1168:
1165:
1162:
1138:
1134:
1130:
1123:
1120:
1111:
1107:
1103:
1096:
1092:
1088:
1085:
1083:
1080:
1068:
1067:
1057:
1047:
1041:
1026:
1022:
1018:
1002:
999:
996:
995:
993:
990:
987:
983:
982:
980:
975:
972:
968:
964:
960:
959:
956:
951:
947:
946:
943:
940:
937:
933:
929:
928:
925:
922:
919:
915:
911:
907:
906:
904:
899:
891:
887:
883:
879:
875:
874:
871:
866:
858:
854:
850:
846:
845:
842:
839:
836:
832:
828:
824:
823:
812:
808:
804:
799:
796:
792:
781:
778:
756:
753:
750:
730:
727:
724:
704:
701:
698:
693:
689:
685:
665:
662:
659:
633:
629:
623:
617:
614:
610:
605:
598:
595:
572:
569:
566:
563:
537:
533:
510:
507:
503:
475:
472:
468:
464:
461:
457:
452:
449:
426:
423:
417:
414:
384:
381:
378:
375:
362:
359:
346:
342:
338:
335:
332:
303:
300:
299:
298:
295:
288:
286:
283:
276:
266:P. W. Anderson
237:Main article:
234:
231:
206:
203:
198:
195:
129:
126:
116:that interact
96:fractionalized
70:
69:
31:
29:
22:
15:
9:
6:
4:
3:
2:
4714:
4703:
4700:
4698:
4695:
4693:
4690:
4688:
4685:
4683:
4680:
4679:
4677:
4657:
4653:
4646:
4631:on 2013-07-28
4627:
4620:
4613:
4598:
4594:
4587:
4579:
4575:
4571:
4567:
4563:
4559:
4555:
4551:
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4541:
4537:
4533:
4529:
4522:
4514:
4510:
4506:
4502:
4498:
4494:
4489:
4484:
4481:(3): 031005.
4480:
4476:
4472:
4465:
4457:
4453:
4449:
4445:
4441:
4437:
4433:
4429:
4424:
4419:
4415:
4411:
4407:
4400:
4386:
4382:
4375:
4361:
4357:
4353:
4349:
4345:
4341:
4337:
4333:
4328:
4323:
4319:
4315:
4311:
4304:
4296:
4292:
4288:
4284:
4280:
4276:
4271:
4266:
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4258:
4257:
4249:
4247:
4238:
4234:
4230:
4226:
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4218:
4214:
4210:
4205:
4200:
4196:
4192:
4184:
4169:
4163:
4157:
4151:
4143:
4139:
4135:
4131:
4127:
4123:
4118:
4113:
4110:(6): 060401.
4109:
4105:
4104:
4084:
4082:
4072:
4067:
4063:
4059:
4055:
4051:
4050:
4045:
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4018:
4013:
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4000:
3996:
3989:
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3977:
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3911:
3907:
3903:
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3895:
3891:
3887:
3883:
3878:
3873:
3869:
3865:
3864:
3856:
3848:
3844:
3840:
3836:
3832:
3828:
3824:
3820:
3815:
3810:
3806:
3802:
3801:
3793:
3791:
3782:
3778:
3774:
3770:
3766:
3762:
3758:
3754:
3749:
3744:
3740:
3736:
3732:
3725:
3717:
3711:
3707:
3703:
3699:
3692:
3690:
3688:
3679:
3675:
3671:
3667:
3663:
3659:
3654:
3649:
3646:(6): 060409.
3645:
3641:
3633:
3625:
3621:
3617:
3613:
3609:
3605:
3601:
3597:
3592:
3587:
3583:
3579:
3572:
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3560:
3556:
3552:
3548:
3544:
3540:
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3531:
3526:
3522:
3518:
3510:
3501:
3496:
3492:
3488:
3483:
3478:
3474:
3470:
3463:
3440:
3432:
3428:
3424:
3420:
3416:
3412:
3407:
3402:
3399:(1): 011001.
3398:
3394:
3375:
3367:
3363:
3359:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3326:
3321:
3317:
3313:
3305:
3297:
3293:
3289:
3285:
3281:
3277:
3273:
3269:
3264:
3259:
3256:(9): 087202.
3255:
3251:
3232:
3224:
3220:
3216:
3212:
3208:
3204:
3200:
3196:
3191:
3186:
3182:
3178:
3177:
3157:
3149:
3145:
3141:
3137:
3133:
3129:
3122:
3114:
3110:
3106:
3102:
3098:
3094:
3090:
3086:
3081:
3076:
3072:
3068:
3061:
3053:
3049:
3045:
3041:
3037:
3033:
3029:
3025:
3018:
3010:
3006:
3002:
2998:
2994:
2990:
2986:
2982:
2978:
2974:
2967:
2959:
2955:
2951:
2947:
2943:
2939:
2934:
2929:
2925:
2921:
2914:
2905:
2901:
2897:
2893:
2889:
2885:
2881:
2877:
2872:
2867:
2863:
2859:
2852:
2844:
2840:
2836:
2832:
2828:
2824:
2820:
2816:
2811:
2806:
2802:
2798:
2779:
2758:
2754:
2749:
2745:
2735:
2727:
2723:
2719:
2715:
2711:
2707:
2703:
2699:
2694:
2689:
2685:
2681:
2674:
2672:
2663:
2659:
2655:
2651:
2647:
2643:
2638:
2633:
2629:
2625:
2618:
2610:
2606:
2602:
2598:
2594:
2590:
2583:
2574:
2566:
2562:
2558:
2554:
2549:
2544:
2541:(4): 041002.
2540:
2536:
2529:
2527:
2525:
2516:
2512:
2508:
2504:
2500:
2496:
2491:
2486:
2482:
2478:
2471:
2463:
2459:
2455:
2451:
2447:
2443:
2438:
2433:
2429:
2425:
2418:
2410:
2406:
2402:
2398:
2394:
2390:
2385:
2380:
2376:
2372:
2365:
2357:
2353:
2349:
2345:
2341:
2337:
2333:
2329:
2322:
2314:
2310:
2306:
2302:
2298:
2294:
2290:
2286:
2279:
2271:
2267:
2263:
2259:
2254:
2249:
2245:
2241:
2237:
2233:
2226:
2218:
2214:
2210:
2206:
2202:
2198:
2194:
2190:
2186:
2179:
2171:
2167:
2163:
2159:
2155:
2151:
2147:
2143:
2136:
2127:
2122:
2118:
2114:
2110:
2103:
2089:
2088:
2083:
2079:
2073:
2059:
2058:
2053:
2049:
2043:
2035:
2031:
2027:
2023:
2019:
2015:
2011:
2007:
2003:
1999:
1995:
1989:
1987:
1985:
1969:
1965:
1958:
1950:
1948:9780521432245
1944:
1939:
1938:
1929:
1921:
1917:
1913:
1909:
1905:
1901:
1897:
1893:
1889:
1885:
1870:
1868:
1852:
1848:
1841:
1833:
1829:
1825:
1821:
1814:
1812:
1810:
1801:
1797:
1793:
1789:
1785:
1781:
1777:
1773:
1768:
1763:
1760:(1): 016502.
1759:
1755:
1748:
1746:
1741:
1734:
1732:
1728:
1718:
1716:
1712:
1708:
1705:
1701:
1700:quasicrystals
1697:
1693:
1689:
1685:
1681:
1677:
1673:
1669:
1665:
1661:
1660:thermodynamic
1656:
1652:
1648:
1644:
1640:
1637:
1633:
1630:
1626:
1623:
1619:
1616:
1612:
1609:
1605:
1601:
1597:
1593:
1589:
1585:
1582:
1579:
1578:quasiparticle
1575:
1572:
1568:
1558:
1556:
1552:
1548:
1538:
1536:
1514:
1500:
1496:
1492:
1488:
1485:
1481:
1477:
1476:heat capacity
1473:
1469:
1465:
1461:
1460:specific heat
1457:
1453:
1449:
1448:heavy fermion
1445:
1441:
1437:
1427:
1425:
1421:
1417:
1413:
1403:
1340:
1297:
1285:
1281:
1279:
1275:
1274:nanoparticles
1270:
1268:
1264:
1260:
1256:
1251:
1249:
1243:
1241:
1237:
1233:
1218:
1214:
1210:
1207:
1204:
1195:
1189:
1174:
1170:
1166:
1163:
1160:
1152:
1151:superexchange
1148:
1144:
1128:
1119:
1117:
1100:
1076:
1072:
1065:
1061:
1058:
1055:
1051:
1048:
1045:
1042:
1039:
1036:
1035:
1034:
1032:
1016:
1012:
1008:
994:
991:
985:
984:
981:
979:
976:
962:
961:
957:
955:
952:
949:
948:
944:
941:
931:
930:
926:
923:
909:
908:
905:
903:
900:
897:
877:
876:
872:
870:
867:
864:
848:
847:
843:
840:
826:
825:
797:
794:
782:
779:
776:
775:
772:
770:
754:
751:
748:
722:
699:
696:
691:
687:
663:
660:
657:
648:
631:
627:
615:
612:
596:
593:
586:
567:
561:
553:
535:
531:
508:
505:
491:
473:
470:
462:
459:
455:
450:
447:
440:
436:
432:
422:
413:
411:
407:
403:
399:
379:
373:
358:
344:
340:
336:
333:
330:
322:
318:
308:
292:
287:
280:
275:
274:
273:
271:
267:
261:
259:
255:
245:
240:
230:
226:
224:
220:
211:
202:
194:
193:excitations.
192:
188:
185:, long-range
184:
179:
178:ferromagnetic
175:
170:
168:
164:
160:
156:
152:
125:
123:
119:
115:
111:
110:Phil Anderson
106:
104:
100:
97:
93:
89:
88:quantum spins
85:
81:
77:
66:
63:
55:
52:December 2012
45:
41:
35:
32:This article
30:
21:
20:
4659:. Retrieved
4655:
4645:
4633:. Retrieved
4626:the original
4612:
4600:. Retrieved
4596:
4586:
4535:
4531:
4521:
4478:
4474:
4464:
4413:
4409:
4399:
4388:. Retrieved
4384:
4374:
4363:. Retrieved
4317:
4313:
4303:
4263:(5): 56001.
4260:
4254:
4194:
4190:
4183:
4171:. Retrieved
4162:
4150:
4107:
4101:
4053:
4047:
4029:
4002:
3998:
3988:
3935:
3929:
3867:
3861:
3855:
3804:
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3738:
3734:
3724:
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3643:
3639:
3632:
3581:
3577:
3571:
3520:
3516:
3509:
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3439:
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3311:
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3253:
3249:
3231:
3180:
3174:
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3121:
3070:
3066:
3060:
3027:
3023:
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2923:
2919:
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2857:
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2800:
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2734:
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2538:
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2476:
2470:
2427:
2423:
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2370:
2364:
2331:
2327:
2321:
2288:
2284:
2278:
2235:
2231:
2225:
2192:
2188:
2178:
2145:
2141:
2135:
2116:
2112:
2102:
2091:. Retrieved
2085:
2072:
2061:. Retrieved
2055:
2042:
2001:
1997:
1994:Leon Balents
1971:. Retrieved
1967:
1957:
1936:
1928:
1887:
1883:
1854:. Retrieved
1850:
1840:
1823:
1819:
1757:
1753:
1724:
1721:Applications
1687:
1683:
1679:
1675:
1654:
1650:
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1638:
1631:
1624:
1617:
1610:
1583:
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1544:
1520:
1490:
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1479:
1471:
1467:
1463:
1455:
1439:
1435:
1433:
1409:
1401:
1271:
1252:
1244:
1190:
1143:rhombohedral
1125:
1101:
1090:
1062:can uncover
1059:
1049:
1043:
1037:
1004:
827:κ-(BEDT-TTF)
649:
584:
552:non-analytic
492:
428:
419:
364:
316:
313:
269:
262:
257:
250:
227:
216:
200:
171:
148:
107:
79:
73:
58:
49:
33:
4661:24 December
4635:24 December
4602:24 December
3938:(2–3): 31.
2926:(11): 790.
2483:: 451–472.
2430:(1): 2–30.
1973:23 December
1856:24 December
1713:exhibiting
1615:temperature
1604:Fermi level
1600:energy band
1588:Topological
1517:Kagome type
942:Hyperkagome
924:Hyperkagome
896:vesignieite
554:feature in
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