Computing general observables in lattice models with complex actions

TL;DR

This paper reviews advanced computational methods for evaluating observables in lattice quantum field theories with complex actions, addressing the sign problem through the density of states and LLR algorithms, with applications to Bose gas and Thirring models.

Contribution

It introduces recent developments in bias control of the LLR method and demonstrates its effectiveness in evaluating complex phase factors in lattice models.

Findings

Successful evaluation of phase factors over hundreds of orders of magnitude in the relativistic Bose gas

Application of the DoS+LLR framework to the Thirring model

Enhanced accuracy in computing observables in complex action systems

Abstract

The study of QFTs at finite density is hindered by the presence of the so-called sign problem. The action definition of such systems is, in fact, complex-valued making standard importance sampling Monte Carlo methods ineffective. In this work, we shall review the generalized density of states method for complex action systems and the Linear Logarithmic Relaxation algorithm (LLR). We will focus on the recent developments regarding the bias control of the LLR method and the evaluation of general observables in the DoS+LLR framework. Recent results on the well-known relativistic Bose gas will be presented, proving that in our approach the phase factor can be consistently evaluated over hundreds of orders of magnitude. A first exploratory study on the Thirring model in the DoS formalism will be presented as well.