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.

48+1 pages, 4 figures. Added and updated some references in v2

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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