Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks

TL;DR

This paper uses tensor networks to simulate a 2D SU(2) Yang-Mills lattice gauge theory with matter, revealing complex phase behavior including baryon liquids and potential topological order.

Contribution

It introduces a sign-problem-free tensor network approach to study the phase diagram of non-Abelian lattice gauge theories with dynamical matter.

Findings

Detection of a baryon liquid phase at intermediate sizes

Observation of potential deconfinement at low quark masses

Signs of topological order at high quark masses

Abstract

We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes (>30 matter sites) well beyond exact diagonalization. We focus on the SU(2) Yang-Mills model in Hamiltonian formulation, with dynamical matter and minimally truncated gauge field (hardcore gluon). Thanks to the TN sign-problem-free approach, we characterize the phase diagram of the model at zero and finite baryon number as a function of the quark bare mass and color charge. At intermediate system sizes, we detect a liquid phase of quark-pair bound-state quasiparticles (baryons), whose mass is finite towards the continuum limit. Interesting phenomena arise at the transition boundary where color-electric and color-magnetic terms are maximally frustrated: For low quark masses, we see traces of potential deconfinement, while for high masses, signatures of a possible topological order.