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 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.

10 pages, 10 figures

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Cited by in corpus (6)

• Probing center vortices and deconfinement in $\mathrm{SU}(2)$ lattice gauge theory with persistent homology
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Probing universal dynamics with topological data analysis in a gluonic plasma
• Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis
• Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
• Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory