Grassmann tensor-network method for strong-coupling QCD

TL;DR

This paper introduces a tensor-network approach for simulating strong-coupling QCD with staggered quarks at nonzero chemical potential, enabling efficient computation of observables and phase transitions in low-dimensional models.

Contribution

The paper develops a Grassmann higher-order tensor renormalization group method tailored for strong-coupling QCD, including validation and preliminary results in three dimensions.

Findings

Validated method against exact results on small lattices

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 method for 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. We apply the method to the two-dimensional case and validate it by comparing results for the partition function, the chiral condensate and the baryon density with exact analytical expressions on small lattices up to volumes of $4\times4$. For larger two-dimensional volumes, we present 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. Furthermore, our results for the number density as a function of the chemical potential hint at a first-order phase transition. Finally, we present some preliminary tensor results for three-dimensional strong-coupling QCD.