Two-color lattice QCD in $(1+1)$ dimensions with Grassmann tensor renormalization group

TL;DR

This paper applies Grassmann tensor renormalization group methods to study two-color lattice QCD in 1+1 dimensions, successfully representing different fermion formulations and analyzing phase transitions at finite density.

Contribution

It introduces tensor network representations for both staggered and Wilson fermions in 1+1D lattice QCD and proposes an efficient gauge degree of freedom compression scheme.

Findings

Computed number density, chiral, and diquark condensates at finite density.

Identified a critical point in the negative mass region for Wilson fermions.

Demonstrated tensor network descriptions with the same bond dimension for different fermion types.

Abstract

The $(1+1)$-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann tensor networks can describe both cases with the same bond dimension. We also propose an efficient initial tensor compression scheme to gauge degrees of freedom. We compute the number density, chiral condensate, and diquark condensate at finite density, employing the staggered fermions. For the theory with Wilson fermion, a critical point in the negative mass region is identified by inspecting the pseudoscalar condensate and the conformal field theory data.