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

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.

23 pages, 11 figures, v2: title changed, new vertex model introduced and studied, more detailed discussion of dualities and other mappings

References in corpus (10)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Topological Order and Conformal Quantum Critical Points
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Entanglement and topological entropy of the toric code at finite temperature
• Topological order in a 3D toric code at finite temperature
• Fragmentation in Frustrated Magnets -- A review
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• The multiple symmetry sustaining phase transitions of spin ice
• Ferromagnetic Coulomb phase in classical spin ice
• Classical vertex model dualities in a family of 2D frustrated quantum antiferromagnets

Cited by in corpus (4)

• Quantum spin ice in three-dimensional Rydberg atom arrays
• Models of interacting bosons with exact ground states: a unified approach
• Breakdown of the thermodynamic limit in quantum spin and dimer models
• Exactly Solvable Topological Phase Transition in a Quantum Dimer Model