Simulating QCD at finite density

TL;DR

This paper reviews the challenges of simulating lattice QCD at finite baryon density, focusing on the sign problem, analytical predictions, and recent progress in understanding the QCD phase diagram.

Contribution

It summarizes current methods to address the sign problem and discusses recent advances in determining the QCD critical point and pseudo-critical temperature.

Findings

Analytical estimates of the sign problem severity

Progress in determining the QCD critical point

Review of non-standard approaches to QCD simulation

Abstract

In this review, I recall the nature and the inevitability of the "sign problem" which plagues attempts to simulate lattice QCD at finite baryon density. I present the main approaches used to circumvent the sign problem at small chemical potential. I sketch how one can predict analytically the severity of the sign problem, as well as the numerically accessible range of baryon densities. I review progress towards the determination of the pseudo-critical temperature T_c(mu), and towards the identification of a possible QCD critical point. Some promising advances with non-standard approaches are reviewed.