Entanglement Properties of Gauge Theories from Higher-Form Symmetries

• URL: http://arxiv.org/abs/2311.16235v2
• Date: Thu, 8 Aug 2024 19:43:11 GMT
• Title: Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Authors: Wen-Tao Xu, Tibor Rakovszky, Michael Knap, Frank Pollmann,
• Abstract summary: We explore the relationship between higher-form symmetries and entanglement properties in discrete lattice gauge theories. Our study centers on the Fradkin-Shenker model, where the Gauss law constraint can be either emergent or exact.
• Score: 2.0936724675062406
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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