Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks

TL;DR

This paper uses tensor network methods to map out the finite-density phase diagram of a (1+1)-dimensional non-abelian SU(2) lattice gauge theory, revealing various phases and phase transitions influenced by matter density and coupling strength.

Contribution

It provides the first detailed numerical characterization of the phase diagram of a non-abelian lattice gauge theory at finite density using tensor networks, including analytical confirmation of some phases.

Findings

Identification of a meson BCS liquid phase at weak coupling

Observation of a charge density wave of mesons at strong coupling and unit filling

Discovery of two tri-critical points consistent with an SU(2)_2 Wess-Zumino-Novikov-Witten model

Abstract

We investigate the finite-density phase diagram of a non-abelian SU(2) lattice gauge theory in (1+1)-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with a $SU(2)_2$ Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the global $U(1)$ charge conservation symmetry.