Interplay of symmetry breaking and deconfinement in 3D quantum vertex models

TL;DR

This paper constructs and analyzes 3D quantum vertex models with complex symmetry and phase behaviors, revealing a gapless point related to quantum spin liquids and exploring the interplay of symmetry breaking and deconfinement.

Contribution

It introduces a broad class of frustration-free 3D quantum vertex models with exact dualities and identifies a gapless point linked to $U(1)$ quantum spin liquids.

Findings

Identification of a gapless point related to the RK point of $U(1)$ spin liquids.

Discovery of a self-duality mapping deconfined and symmetry-broken phases.

Observation of an intermediate phase where symmetry breaking and deconfinement coexist.

Abstract

We construct a broad class of frustration-free quantum vertex models in 3+1D whose ground states are weighted superpositions of classical 3D vertex model configurations. Our results are illustrated for diamond, cubic, and BCC lattices, but hold for general 3D lattices with even coordination number. The corresponding classical vertex models have a $\mathbb{Z}_2$ gauge constraint enriched with a $\mathbb{Z}_2$ global symmetry. We study the interplay between these symmetries by exploiting exact wavefunction dualities and effective field theories. We find an exact gapless point which by duality is related to the Rokhsar-Kivelson (RK) point of $U(1)$ quantum spin liquids. At this point, both the symmetry breaking and deconfinement order parameters exhibit long range order. The gapless point is additionally a self-dual point of a second duality that maps the $\mathbb{Z}_2$ deconfined and $\mathbb{Z}_2$ symmetry-broken phases to one another. For the BCC lattice vertex model, we find that gapless point is proximate to an unusual intermediate phase where symmetry breaking and deconfinement coexist.