Extended mean field study of complexφ4-theory at finite density and temperature

Oscar Akerlund,Philippe De Forcrand,Philipp Werner,Antoine Georges

doi:10.1103/physrevd.90.065008

Abstract

We review the extended mean field theory (EMFT) approximation and apply it to complex, scalar ${\ensuremath{\varphi}}^{4}$ theory on the lattice. We study the critical properties of the Bose condensation driven by a nonzero chemical potential $\ensuremath{\mu}$ at both zero and nonzero temperature and determine the $(T,\ensuremath{\mu})$ phase diagram. The results are in very good agreement with recent Monte Carlo data for all parameter values considered. EMFT can be formulated directly in the thermodynamic limit which allows us to study lattice spacings for which Monte Carlo studies are not feasible with present techniques. We find that the EMFT approximation accurately reproduces many known phenomena of the exact solution, like the ``Silver Blaze'' behavior at zero temperature and dimensional reduction at finite temperature.

Highlights

One serious obstacle in lattice field theory and computational physics is the so-called “sign problem,” which spoils the probabilistic interpretation of the partition function and a foundation of the otherwise powerful Monte Carlo method
We review the extended mean field theory (EMFT) approximation and apply it to complex, scalar φ4 theory on the lattice
We find that the EMFT approximation accurately reproduces many known phenomena of the exact solution, like the “Silver Blaze” behavior at zero temperature and dimensional reduction at finite temperature

Summary

Introduction

One serious obstacle in lattice field theory and computational physics is the so-called “sign problem,” which spoils the probabilistic interpretation of the partition function and a foundation of the otherwise powerful Monte Carlo method. The statistics of the fields might cause some configurations to appear with a negative (fermions) or complex (anyons) weight. While it is possible, in principle, to consider suitable subsets of the configuration space [1] or to use another set of variables [2] to end up with only non-negative weights, appropriate subsets or new variables have only been found for a small number of models so far. The sign problem can sometimes be solved by considering a different set of variables, like in the world-line Monte Carlo approach [3,4]. Recent progress in the understanding of the complex Langevin equations [5,6] and gauge cooling [7] has promoted yet another approach for simulating models with complex actions

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