New approach to lattice QCD at finite density: reweighting without an overlap problem

TL;DR

This paper introduces a sign reweighting method for finite density lattice QCD that avoids the overlap problem, enabling reliable exploration of the phase diagram where other methods fail.

Contribution

The authors propose and test a sign reweighting approach that directly addresses the sign problem in lattice QCD at finite density, avoiding uncontrolled systematic uncertainties.

Findings

Successfully applied the method to locate the critical endpoint with unimproved staggered fermions.

Studied the phase diagram with improved staggered fermions on a finer lattice, relevant for phenomenology.

Demonstrated the method's ability to explore regions inaccessible to Taylor and imaginary chemical potential methods.

Abstract

Approaches to finite baryon density lattice QCD usually suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We test a method - sign reweighting - that works directly at finite chemical potential and is yet free from any such uncontrolled systematics: with this approach the only problem is the sign problem itself. In practice the approach involves the generation of configurations with the positive fermionic weights given by the absolute value of the real part of the quark determinant, and a reweighting by a sign. There are only two sectors, +1 and -1 and as long as the average $\left\langle \pm \right\rangle \neq 0$ (with respect to the positive weight) this discrete reweighting has no overlap problem - unlike reweighting from $\mu=0$ - and the results are reliable. We also present results based on this algorithm on the phase diagram of lattice QCD with two different actions: as a first test, we apply the method to calculate the position of the critical endpoint with unimproved staggered fermions at $N_\tau=4$; as a second application, we study the phase diagram with 2stout improved staggered fermions at $N_\tau=6$. This second one is already a reasonably fine lattice - relevant for phenomenology. We demonstrate that the method penetrates the region of the phase diagram where the Taylor and imaginary chemical potential methods lose predictive power.