Tensor renormalization group study of cold and dense QCD in the strong coupling limit

TL;DR

This paper employs the tensor renormalization group method to analyze the phase structure of cold, dense QCD in the strong coupling limit, identifying critical quark masses and phase transition characteristics.

Contribution

It introduces a tensor renormalization group approach to study the phase transitions in (3+1)-dimensional cold dense QCD at strong coupling, providing new insights into critical quark masses and phase behavior.

Findings

Critical quark masses for chiral and nuclear transitions are determined.

First-order phase transition confirmed at finite quark mass on large lattice.

Results are consistent with Monte Carlo and mean-field analyses.

Abstract

We study the phase structure of the (3+1)-dimensional cold and dense QCD with the Kogut--Susskind quark in the strong coupling limit using the tensor renormalization group method. The chiral and nuclear transitions are investigated by calculating the chiral condensate and the quark number density as a function of the chemical potential. For a fixed temporal extent $N_\tau=8$, we determine the critical quark masses $m_c^{\chi}$ and $m_c^{n}$ for the chiral condensate and the quark number density, respectively, at which the first-order phase transition terminates with the vanishing discontinuity in thermodynamic quantities. We find that both quantities at the same quark mass exhibit a discontinuity at the same chemical potential, and the resulting critical quark masses are consistent with each other. We also compare our results for the critical quark masses with those obtained from the Monte Carlo simulation in the dual formulation and from the mean-field analysis. We further confirm the first-order phase transition at finite quark mass on a $1024^4$ lattice, which is essentially in the thermodynamic limit at zero temperature, as expected from the mean-field analysis.