Grassmann tensor approach for two-dimensional QCD in the strong-coupling expansion

TL;DR

This paper introduces a tensor-network method for analyzing two-dimensional QCD at strong coupling, enabling exact gauge field integration and computation of physical observables at non-zero chemical potential.

Contribution

The authors develop a Grassmann tensor network approach that extends the strong-coupling expansion of 2D QCD, allowing for systematic calculations of quark density and chiral condensate.

Findings

Accurate computation of quark number density and chiral condensate up to order β^3.

Method effectively extends the valid range of the strong-coupling expansion.

Provides a new expansion in β for the critical chemical potential.

Abstract

We present a tensor-network approach for the strong-coupling expansion of two-dimensional QCD with staggered quarks at non-zero chemical potential. After expanding the Boltzmann factor in the gauge and fermion actions, all gauge fields can be integrated out exactly and the partition function can be evaluated using the Grassmann higher-order tensor renormalization group approach. The method is modified to compute the $\mu$ dependence of the quark number density and the chiral condensate up to order $\beta^3$ with complete absence of higher-order terms infiltrating the result. Although the expansion itself is only a good approximation to the full theory at small $\beta<0.1$, the range can be extended, by using judiciously chosen fits. Moreover, these fits also yield a valuable expansion in $\beta$ for the critical chemical potential.