Tensor-network formulation of QCD in the strong-coupling expansion

TL;DR

This paper develops a tensor-network approach for analyzing the strong-coupling expansion of QCD with staggered quarks at nonzero chemical potential, enabling analytical and numerical insights into lattice gauge theories.

Contribution

It introduces a tensor-network formulation for QCD in the strong-coupling regime, including a truncation scheme and initial analytical results on small lattices.

Findings

Analytical results for partition function, free energy, and chiral condensate on a 2x2 lattice.

Tensor network representation includes local tensors with numerical and Grassmann parts.

Initial results demonstrate the potential of the new tensor-network method for larger lattices.

Abstract

We present a tensor-network formulation for the strong-coupling expansion of QCD with staggered quarks at nonzero chemical potential, for arbitrary number of dimensions, colors, and flavors. We integrate out the gauge and quark degrees of freedom and rewrite the partition function as the complete trace of a tensor network. This network consists of local tensors that contain a numerical and a Grassmann part. We truncate the initial tensor at a fixed order in the inverse coupling $\beta$ and compute analytical results for the partition function, the free energy, and the chiral condensate on a $2\times2$ lattice up to order $\beta^4$. In a follow-up paper we will introduce an enhanced tensor-network method, order-separated GHOTRG, to explicitly compute the expansion coefficients of the partition function for larger lattices. To demonstrate its potential, first results obtained with this new method are already presented here.