A general approach to the sign problem - the factorization method with multiple observables

Abstract

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control some observables in order to determine and sample efficiently the region of configuration space which gives important contribution to the partition function. We argue that it is crucial to choose appropriately the set of the observables to be controlled in order for the method to work successfully in a general system. This is demonstrated by an explicit example, in which it turns out to be necessary to control more than one observables. Extrapolation to large system size is possible due to the nice scaling properties of the factorized functions, and known results obtained by an analytic method are shown to be consistently reproduced.

6 pages, 3 figures, (v2) references added (v3) Sections IV, V and VI improved, final version accepted by PRD

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• Introductory lectures on lattice QCD at nonzero baryon number
• Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Progress in the numerical studies of the type IIB matrix model
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Matrix geometries and Matrix Models
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• The origin of space-time as seen from matrix model simulations
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• Recent developments in the type IIB matrix model
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• Taming the pion condensation in QCD at finite baryon density
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking