Duality-preserving deformation of 3+1d lattice ${\mathbb{Z}}_2$ gauge theory with exact gapped ground states

Abstract

We propose and analyze a deformation of the 3+1d lattice ${\mathbb{Z}}_2$ gauge theory that preserves the non-invertible Wegner duality symmetry at the self-dual point. We identify a frustration-free point along this deformation where there are nine exactly degenerate ground states (on a periodic cubic lattice) even at finite volume. One of these ground states is a trivial product state and the rest are the topologically-ordered ground states of the 3+1d toric code. We also prove that the frustration-free point is gapped in the thermodynamic limit. Our model, therefore, realizes a gapped phase with spontaneously broken Wegner duality symmetry. Furthermore, by imposing the Gauss law constraints energetically, all the above features can be realized on a tensor product Hilbert space. Finally, we discuss a generalization of this deformation to the 3+1d lattice ${\mathbb{Z}}_N$ gauge theory and conjecture the possible phase diagram.

arXiv comment48+1 pages, 4 figures. Added and updated some references in v2

References in corpus (42)

• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• Interacting Quantum Observables: Categorical Algebra and Diagrammatics
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Duality Defects in 3+1 Dimensions
• Undecidability of the Spectral Gap (short version)
• Topological Defects on the Lattice I: The Ising model
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Phase Diagram of the Interacting Majorana Chain Model
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• The spectral gap for some spin chains with discrete symmetry breaking
• Long-range entanglement from measuring symmetry-protected topological phases
• Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• Non-Invertible Duality Transformation Between SPT and SSB Phases
• On lattice models of gapped phases with fusion category symmetries
• Topological conformal defects with tensor networks
• Cluster state as a non-invertible symmetry protected topological phase
• Higher categorical symmetries and gauging in two-dimensional spin systems
• Subsystem Non-Invertible Symmetry Operators and Defects
• Local gap threshold for frustration-free spin systems
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
• Sequential Quantum Circuits as Maps between Gapped Phases
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Non-invertible symmetries act locally by quantum operations
• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
• Generating Lattice Non-invertible Symmetries
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Constraints on order and disorder parameters in quantum spin chains
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
• Divide and conquer method for proving gaps of frustration free Hamiltonians
• Topological Defects in Floquet Circuits
• Undecidability of the Spectral Gap (full version)
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Non-integrable Floquet Ising model with duality twisted boundary conditions

Cited by in corpus (3)

• Duality defect in a deformed transverse-field Ising model
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d
• Non-onsite symmetry breaking: topological phase coexistence and criticality