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A new method to study lattice QCD at finite temperature and chemical potential

Z. Fodor, S. D. Katz

TL;DR

The paper addresses the sign problem in lattice QCD at finite chemical potential by introducing an overlap-improving multi-parameter reweighting technique that reweights in multiple parameters (notably $\beta$ and $\mu$) using an ensemble generated at a reference point. This approach, which leverages $Z(\alpha)$ and determinants $\det M(\phi,\alpha)$ along with Ferrenberg-Swendsen-like reweighting and Lee-Yang zero analysis, enables tracing the transition line in the $T$-$\mu$ plane even at nonzero real $\mu$ and imaginary $\beta$. The method is tested on $n_f=4$ dynamical QCD with staggered quarks on small lattices ($4^4$ and $4\cdot6^3$), showing agreement with direct simulations for imaginary $\mu$ and improved overlap relative to the Glasgow method; a $T$-$\mu$ phase diagram is extracted in physical units using $m_\rho=770$ MeV. While the results are exploratory and limited by small volumes and coarse spacing, the technique provides a practical tool for locating a potential critical point in regions of relatively small $\mu$ and higher $T$, and can be adapted to other fermion discretizations.

Abstract

Due to the sign problem, it is exponentially difficult to study QCD on the lattice at finite chemical potential. We propose a method --an overlap improving multi-parameter reweighting technique-- to alleviate this problem. We apply this method and give the phase diagram of four-flavor QCD obtained on lattices 4^4 and 4\cdot6^3. Our results are based on {\cal{O}}(10^3-10^4) configurations.

A new method to study lattice QCD at finite temperature and chemical potential

TL;DR

The paper addresses the sign problem in lattice QCD at finite chemical potential by introducing an overlap-improving multi-parameter reweighting technique that reweights in multiple parameters (notably and ) using an ensemble generated at a reference point. This approach, which leverages and determinants along with Ferrenberg-Swendsen-like reweighting and Lee-Yang zero analysis, enables tracing the transition line in the - plane even at nonzero real and imaginary . The method is tested on dynamical QCD with staggered quarks on small lattices ( and ), showing agreement with direct simulations for imaginary and improved overlap relative to the Glasgow method; a - phase diagram is extracted in physical units using MeV. While the results are exploratory and limited by small volumes and coarse spacing, the technique provides a practical tool for locating a potential critical point in regions of relatively small and higher , and can be adapted to other fermion discretizations.

Abstract

Due to the sign problem, it is exponentially difficult to study QCD on the lattice at finite chemical potential. We propose a method --an overlap improving multi-parameter reweighting technique-- to alleviate this problem. We apply this method and give the phase diagram of four-flavor QCD obtained on lattices 4^4 and 4\cdot6^3. Our results are based on {\cal{O}}(10^3-10^4) configurations.

Paper Structure

This paper contains 4 sections, 2 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Overlap improving multi-parameter reweighting
  3. Illustration: $n_f$=4 dynamical QCD results
  4. Conclusions, outlook

Figures (3)

  • Figure 1: The average of the quark condensates at $\beta$=5.085 as a function of Im($\mu$), for direct simulations (squares; their sizes give the errors), our technique (crosses) and Glasgow-type reweighting (dots).
  • Figure 2: The average of the Polyakov lines (squares) and quark condensates (triangles) as a function of $\beta$ at ${\rm Im}(\mu)=0,\ {\rm Re}(\mu)=0.3$ (left panel). Histogram of the plaquettes at $\beta$=4.938 and $\mu$=0.3 (right panel). The lattice volume is $4^4$.
  • Figure 3: The phase diagram in the $T$-$\mu$ plane for $n_f=4$ QCD. The physical scale is set by $m_\rho$. In physical units $m_q\approx$ 25 MeV. The last point ($\mu \approx$190 MeV) corresponds to our largest reweighted $\mu$.