Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD

TL;DR

This paper introduces a tensor-network method using Grassmann higher-order tensor renormalization group techniques to study two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential, enabling analysis of phase transitions.

Contribution

The paper develops a novel Grassmann higher-order tensor renormalization group approach tailored for 2D strong-coupling QCD, including analytical tensor blocking and validation against exact results.

Findings

Validated the method on small lattices with exact results.

Observed no spontaneous chiral symmetry breaking in 2D.

Indications of a first-order phase transition at finite chemical potential.

Abstract

We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of a tensor network consisting of coupled local numeric and Grassmann tensors. To evaluate the partition function and to compute observables, we develop a Grassmann higher-order tensor renormalization group method, specifically tailored for this model. During the coarsening procedure, the blocking of adjacent Grassmann tensors is performed analytically, and the total number of Grassmann variables in the tensor network is reduced by a factor of two at each coarsening step. The coarse-site numeric tensors are truncated using higher-order singular value decompositions. The method is validated by comparing the partition function, the chiral condensate and the baryon density computed with the tensor method with exact analytical results on small lattices up to volumes of $4\times4$. For larger volumes, we present first tensor results for the chiral condensate as a function of the mass and volume, and observe that the chiral symmetry is not broken dynamically in two dimensions. We also present tensor results for the number density as a function of the chemical potential, which hint at a first-order phase transition.