Grassmann tensor renormalization group approach to $(1+1)$-dimensional two-color lattice QCD at finite density

TL;DR

This paper develops a Grassmann tensor network method to study (1+1)-dimensional two-color lattice QCD at finite density, enabling efficient computation of physical observables across different parameters.

Contribution

It introduces a novel Grassmann tensor network construction and an efficient tensor compression scheme for analyzing lattice QCD at finite density.

Findings

Observed different phase transition behaviors with varying quark mass.

Successfully computed quark number density, condensates, and diquark condensates.

Demonstrated the efficiency of tensor compression in the tensor renormalization group approach.

Abstract

We construct a Grassmann tensor network representing the partition function of (1+1)-dimensional two-color QCD with staggered fermions. The Grassmann path integral is rewritten as the trace of a Grassmann tensor network by introducing two-component auxiliary Grassmann fields on every edge of the lattice. We introduce an efficient initial tensor compression scheme to reduce the size of initial tensors. The Grassmann bond-weighted tensor renormalization group approach is adopted to evaluate the quark number density, fermion condensate, and diquark condensate at different gauge couplings as a function of the chemical potential. Different transition behavior is observed as the quark mass is varied. We discuss the efficiency of our initial tensor compression scheme and the future application toward the corresponding higher-dimensional models.