Overcoming the sign problem in 1-dimensional QCD by new integration rules with polynomial exactness

Abstract

In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov Chain Monte Carlo fails in this region, our new integration method still provides results for the chiral condensate on arbitrary precision, demonstrating clearly that it overcomes the sign problem. Furthermore, we demonstrate that our new method leads to orders of magnitude reduced errors also in other regions of parameter space.

arXiv commentadded reference in introduction

References in corpus (8)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Approaches to the sign problem in lattice field theory
• Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential
• Subset method for one-dimensional QCD
• QCD in One Dimension at Nonzero Chemical Potential
• Subsets and the canonical partition functions
• Quasi-Monte Carlo methods for lattice systems: a first look
• On the efficient numerical solution of lattice systems with low-order couplings

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