Perturbative Removal of a Sign Problem

Abstract

This paper presents a method for alleviating sign problems in lattice path integrals, including those associated with finite fermion density in relativistic systems. The method makes use of information gained from some systematic expansion -- such as perturbation theory -- in order to accelerate the Monte Carlo. The method is exact, in the sense that no approximation to the lattice path integral is introduced. Thanks to the underlying systematic expansion, the method is systematically improvable, so that an arbitrary reduction in the sign problem can in principle be obtained. The Thirring model (in 0 + 1 and 1 + 1 dimensions) is used to demonstrate the ability of this method to reduce the finite-density sign problem.

arXiv comment7 pages, 4 figures

References in corpus (16)

• The QCD thermal phase transition in the presence of a small chemical potential
• A new method to study lattice QCD at finite temperature and chemical potential
• The chiral critical line of N_f=2+1 QCD at zero and non-zero baryon density
• Lattice QCD at finite density via a new canonical approach
• Finite density QCD with a canonical approach
• Stochastic quantization at finite chemical potential
• A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
• Monte Carlo study of real time dynamics
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Monte Carlo calculations of the finite density Thirring model
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• Path integral contour deformations for noisy observables
• Thirring model at finite density in 2+1 dimensions with stochastic quantization
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• The worm process for the Ising model is rapidly mixing
• Simple QED- and QCD-like Models at Finite Density

Cited by in corpus (6)

• Normalizing Flows and the Real-Time Sign Problem
• Sign Problem in Quantum Monte Carlo Simulation
• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Gauge invariant input to neural network for path optimization method
• Deep Learning of Fermion Sign Fluctuations
• Optimisation of complex integration contours at higher order