Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds

TL;DR

This paper introduces a sign-optimized manifold approach to perform Monte Carlo simulations of the (2+1)d Thirring model at finite density, overcoming the sign problem and revealing phase transitions in thermodynamics.

Contribution

It develops a novel complex manifold deformation technique to mitigate the sign problem in finite density fermion simulations.

Findings

Chiral condensate drops sharply at high densities and temperatures

Method enables simulations on larger lattices up to 10^3

Provides insights into phase transitions in (2+1)d fermionic systems

Abstract

We present Monte Carlo calculations of the thermodynamics of the (2+1) dimensional Thirring model at finite density. We bypass the sign problem by deforming the domain of integration of the path integral into complex space in such a way as to maximize the average sign within a parameterized family of manifolds. We present results for lattice sizes up to $10^3$ and we find that at high densities and/or temperatures the chiral condensate is abruptly reduced.