169:. Similar factors arise also in quantum field theories; however, these can have indefinite sign (especially in the case of Fermions) or even be complex-valued, which precludes their direct interpretation as probabilities. In these cases, one has to resort to a reweighting procedure (i.e., interpret the absolute value as probability and multiply the sign or phase to the observable) to get a strictly positive reference distribution suitable for Monte Carlo sampling. However, it is well known that, in specific parameter ranges of the model under consideration, the oscillatory nature of the weight function can lead to a bad
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configurations. In this sense, there is a trade-off: instead of dealing with one very complicated many-body problem, one faces the calculation of an infinite number of simple external-field problems.
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Baeurle, S.A. (2003a). "The stationary phase auxiliary field Monte Carlo method: a new strategy for reducing the sign problem of auxiliary field methodologies".
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Baer, R.; Head-Gordon, M.; Neuhauser, D. (1998). "Shifted-contour auxiliary field Monte Carlo for ab initio electronic structure: Straddling the sign problem".
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Baeurle, S.A.; Martonak, R.; Parrinello, M. (2002a). "A field-theoretical approach to simulation in the classical canonical and grand canonical ensemble".
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Baeurle, S.A. (2002). "Method of
Gaussian Equivalent Representation: A New Technique for Reducing the Sign Problem of Functional Integral Methods".
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The distinctive ingredient of "auxiliary-field Monte Carlo" is the fact that the interactions are decoupled by means of the application of the
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Baeurle, S.A. (2004). "Grand canonical auxiliary field Monte Carlo: a new technique for simulating open systems at high density".
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Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L. (1981). "Monte Carlo calculations of coupled boson-fermion systems. I".
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Ceperley, D.; Chester, G.V.; Kalos, M.H. (1977). "Monte Carlo simulation of a many-fermion study".
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Baeurle, S.A. (2003). "Computation within the auxiliary field approach".
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and can be alleviated with analytical and numerical
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227:but its sources remain unclear because it lacks
126:Reweighting procedure and numerical sign problem
48:introducing citations to additional sources
185:procedures (Baeurle 2002, Baeurle 2003a).
258:Learn how and when to remove this message
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116:Monte Carlo techniques
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