Duality-preserving deformation of 3+1d lattice $\mathbb Z_2$ gauge theory with exact gapped ground states

• URL: http://arxiv.org/abs/2409.10612v1
• Date: Mon, 16 Sep 2024 18:00:03 GMT
• Title: Duality-preserving deformation of 3+1d lattice $\mathbb Z_2$ gauge theory with exact gapped ground states
• Authors: Pranay Gorantla, Tzu-Chen Huang,
• Abstract summary: We analyze a deformation of the 3+1d lattice $mathbb Z$ gauge theory. We find nine exactly degenerate ground states (on a periodic cubic lattice) even at finite volume. Our model realizes a gapped phase with spontaneously broken Wegner duality symmetry.
• Score: 0.1534667887016089
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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