Persistent Homology Analysis for Dense QCD Effective Model with Heavy Quarks

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 dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it the QCD-like Potts model. The QCD-like Potts model does not have a sign problem, but we expect it to share 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 toward 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 where the birth-death ratio means the ratio of the creation time of a hole and its vanishing time based on the persistent homology.

Probing universal dynamics with topological data analysis in a gluonic plasma

“…A first study of persistent homology dynamics in the vicinity of a nonthermal fixed point in scalar field theory demonstrated its ability to reveal self-similar behavior [43]. Persistent homology has been applied in the related context of critical phenomena [44][45][46][47][48][49][50][51], notably confinement in non-Abelian gauge theory [52,53] and corresponding effective models [54,55].…”