A new dual representation for staggered lattice QCD

TL;DR

This paper introduces a novel dual representation for lattice QCD with Wilson gauge action and staggered fermions, enabling systematic strong coupling expansions and potential mitigation of the finite density sign problem.

Contribution

It develops a new dual formulation using Decoupling Operator Indices, transforming the partition function into a tensor network suitable for worm-like algorithms.

Findings

Exact rewriting of the partition function in terms of DOI

Tensor network representation for simulation

Framework for higher order $eta$-corrections

Abstract

We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling $\beta= 2N/g^{2}$. Our method makes use of the recently developed formalism to evaluate the ${\rm SU}(N)$ $1-$link integrals and consists in an exact rewriting of the partition function in terms of a set of additional dual degrees of freedom which we call "Decoupling Operator Indices" (DOI). The method is not limited to any particular number of dimensions or gauge group ${\rm U}(N)$, ${\rm SU}(N)$. In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Worm-like algorithms. Higher order $\beta$-corrections to strong coupling lattice QCD can be, in principle, systematically evaluated, helping to answer the question whether the finite density sign problem remains mild when plaquette contributions are included. Issues related to the complexity of the description and strategies for the stochastic evaluation of the partition function are discussed.