Persistent homology analysis for dense QCD effective model with heavy quarks

TL;DR

This paper introduces a QCD-like Potts model with isospin chemical potential and uses persistent homology to analyze its spatial structure, revealing insights related to phase transitions without sign problems.

Contribution

The study applies persistent homology to a dense QCD effective model with heavy quarks, providing new topological insights into phase transition phenomena.

Findings

Birth-death ratio correlates with Polyakov loop

Maximum birth-death ratio signals phase transition

Persistent homology captures dense spatial structures

Abstract

The isospin chemical potential region is known as the sign-problem free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic the dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it as QCD-like Potts model. The QCD-like Potts model does not have the sign problem, but we can expect that it shares some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential where the simple Metropolis algorithm can work, we perform the persistent homology analysis towards exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition.