Effective $\mathbb{Z}_{3}$ model for finite-density QCD with tensor networks

TL;DR

This paper applies tensor renormalization group techniques to an effective $ ext{Z}_3$ model of finite-density QCD, providing a computationally efficient way to explore its phase diagram and validating results with Monte Carlo methods.

Contribution

It introduces a tensor network approach to study a simplified $ ext{Z}_3$ model for finite-density QCD, offering a new computational method in this context.

Findings

Phase diagram mapped using tensor renormalization group.

Results agree with existing literature and Monte Carlo simulations.

Demonstrates tensor networks as a viable tool for finite-density QCD studies.

Abstract

The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group methods to study an effective three-dimensional $\mathbb{Z}_{3}$ model for the heavy-quark, high-temperature, strong-coupling limit of single-flavor 3+1 dimensional quantum chromodynamics. Our results are cross-checked using the worm Monte Carlo algorithm. We present the phase diagram of the model through the measurement of the Polyakov loop, the nearest-neighbor Polyakov loop correlator, and their susceptibilities. The tensor renormalization group results are in good agreement with the literature