Tensor renormalization group study of (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density

Abstract

We investigate the critical endpoints of the (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density together with the (2+1)-dimensional one at zero density as a benchmark using the tensor renormalization group method. We focus on the phase transition between the Higgs phase and the confinement phase at finite chemical potential along the critical end line. In the (2+1)-dimensional model, the resulting endpoint is consistent with a recent numerical estimate by the Monte Carlo simulation. In the (3+1)-dimensional case, however, the location of the critical endpoint shows disagreement with the known estimates by the mean-field approximation and the Monte Carlo studies. This is the first application of the tensor renormalization group method to a four-dimensional lattice gauge theory and a key stepping stone toward the future investigation of the phase structure of the finite density QCD.

21 pages, 15 figures

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Cited by in corpus (10)

• Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory
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• Phase diagram of generalized XY model using tensor renormalization group
• GrassmannTN: a Python package for Grassmann tensor network computations
• Tensor renormalization group approach to (1+1)-dimensional SU(2) principal chiral model at finite density
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Grassmann tensor renormalization group approach to $(1+1)$-dimensional two-color lattice QCD at finite density
• Spectroscopy with the tensor renormalization group method
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method