Duality-preserving deformation of 3+1d lattice $\mathbb Z_2$ gauge theory with exact gapped ground states
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| Format: | Preprint |
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2024
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| _version_ | 1866911380854013952 |
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| author | Gorantla, Pranay Huang, Tzu-Chen |
| author_facet | Gorantla, Pranay Huang, Tzu-Chen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_10612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality-preserving deformation of 3+1d lattice $\mathbb Z_2$ gauge theory with exact gapped ground states Gorantla, Pranay Huang, Tzu-Chen Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics 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. |
| title | Duality-preserving deformation of 3+1d lattice $\mathbb Z_2$ gauge theory with exact gapped ground states |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2409.10612 |