Entanglement Properties of Gauge Theories from Higher-Form Symmetries
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910770843877376 |
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| author | Xu, Wen-Tao Rakovszky, Tibor Knap, Michael Pollmann, Frank |
| author_facet | Xu, Wen-Tao Rakovszky, Tibor Knap, Michael Pollmann, Frank |
| contents | We explore the relationship between higher-form symmetries and entanglement properties in discrete lattice gauge theories, which can exhibit both topologically ordered phases and higher-form symmetry-protected topological (SPT) phases. Our study centers on generalizing the Fradkin-Shenker model, where the Gauss law constraint can be either emergent or exact. The phase diagram includes a topologically ordered phase and a non-trivial SPT phase protected by a 1-form and a 0-form symmetry. We obtain the following key findings: First, the entanglement properties depend on whether the 1-form symmetries and the Gauss law are exact or emergent. For the emergent Gauss law, the entanglement spectrum (ES) of the non-trivial SPT phase exhibits degeneracies, which are robust at low energies against weak perturbations that explicitly break the exact 1-form symmetry. When the Gauss law and the 1-form symmetry are both exact, the ES degeneracy is extensive. This extensive degeneracy is fragile and can be removed completely by infinitesimal perturbations that explicitly break the exact 1-form symmetry while keeping the Gauss law exact. Second, we consider the ES in the topologically ordered phase where 1-form symmetries are spontaneously broken. In contrast to the ES of the non-trivial SPT phase, we find that spontaneous higher-form symmetry breaking removes "half" of the ES levels, leading to a non-degenerate ES in the topologically ordered phase in general. Third, we derive a connection between spontaneous higher-form symmetry breaking and the topological entanglement entropy (TEE). Using this relation, we investigate the entanglement entropy that can be distilled in the deconfined phase of the original Fradkin-Shenker model using gauge-invariant measurements. We show that the TEE is robust against the measurement when the 1-form symmetry is emergent but fragile when the 1-form symmetry is exact. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_16235 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entanglement Properties of Gauge Theories from Higher-Form Symmetries Xu, Wen-Tao Rakovszky, Tibor Knap, Michael Pollmann, Frank Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice Quantum Physics We explore the relationship between higher-form symmetries and entanglement properties in discrete lattice gauge theories, which can exhibit both topologically ordered phases and higher-form symmetry-protected topological (SPT) phases. Our study centers on generalizing the Fradkin-Shenker model, where the Gauss law constraint can be either emergent or exact. The phase diagram includes a topologically ordered phase and a non-trivial SPT phase protected by a 1-form and a 0-form symmetry. We obtain the following key findings: First, the entanglement properties depend on whether the 1-form symmetries and the Gauss law are exact or emergent. For the emergent Gauss law, the entanglement spectrum (ES) of the non-trivial SPT phase exhibits degeneracies, which are robust at low energies against weak perturbations that explicitly break the exact 1-form symmetry. When the Gauss law and the 1-form symmetry are both exact, the ES degeneracy is extensive. This extensive degeneracy is fragile and can be removed completely by infinitesimal perturbations that explicitly break the exact 1-form symmetry while keeping the Gauss law exact. Second, we consider the ES in the topologically ordered phase where 1-form symmetries are spontaneously broken. In contrast to the ES of the non-trivial SPT phase, we find that spontaneous higher-form symmetry breaking removes "half" of the ES levels, leading to a non-degenerate ES in the topologically ordered phase in general. Third, we derive a connection between spontaneous higher-form symmetry breaking and the topological entanglement entropy (TEE). Using this relation, we investigate the entanglement entropy that can be distilled in the deconfined phase of the original Fradkin-Shenker model using gauge-invariant measurements. We show that the TEE is robust against the measurement when the 1-form symmetry is emergent but fragile when the 1-form symmetry is exact. |
| title | Entanglement Properties of Gauge Theories from Higher-Form Symmetries |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2311.16235 |