Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion

TL;DR

This paper introduces two efficient hopping parameter expansions for simulating QCD at nonzero baryon density, demonstrating their effectiveness with complex Langevin dynamics and supporting their convergence and applicability.

Contribution

It presents two all-orders hopping parameter expansions that are computationally cheaper and compatible with complex Langevin dynamics for simulating QCD at finite density.

Findings

Agreement between expanded and full theory at high order

Support for complex Langevin dynamics in finite density QCD

Validation of convergence of hopping expansions

Abstract

Progress in simulating QCD at nonzero baryon density requires, amongst others, substantial numerical effort. Here we propose two different expansions to all orders in the hopping parameter, preserving the full Yang-Mills action, which are much cheaper to simulate. We carry out simulations using complex Langevin dynamics, both in the hopping expansions and in the full theory, for two flavours of Wilson fermions, and agreement is seen at sufficiently high order in the expansion. These results provide support for the use of complex Langevin dynamics to study QCD at nonzero density, both in the full and the expanded theory, and for the convergence of the latter.