Advances in non-relativistic matter via complex Langevin approaches

TL;DR

This paper reviews recent advances in applying complex Langevin methods to non-relativistic many-body physics, addressing the sign problem in various one-dimensional systems with different interaction parameters.

Contribution

It highlights new applications of complex Langevin techniques to non-relativistic matter, expanding their use beyond relativistic quantum field theories.

Findings

Improved understanding of thermodynamics in non-relativistic systems with sign problems

Application of complex Langevin to systems with repulsive interactions and polarization

Calculation of virial coefficients for finite systems

Abstract

The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened up an intriguing possibility for non-relativistic many-body physics which has so far remained largely unexplored. In this brief contribution, I review a few specific examples of advances in the characterization of the thermodynamics of non-relativistic matter in a variety of one-dimensional cases affected by the sign problem: repulsive interactions, finite polarization, finite mass imbalance, and projection to finite systems to obtain virial coefficients.