Entanglement Properties of Gauge Theories from Higher-Form Symmetries

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.

Add the ES transition near the 1-form SPT phase. Add understanding of our results from 1-form symmetries

References in corpus (17)

• Generalized Global Symmetries
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Generalized Symmetries in Condensed Matter
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Pivot Hamiltonians as generators of symmetry and entanglement
• Gauging the Kitaev chain
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Exact emergent higher-form symmetries in bosonic lattice models
• Fragility of Symmetry Protected Topological Order on a Hubbard Ladder
• Revisiting Entanglement Entropy of Lattice Gauge Theories
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Quantum entanglement in states generated by bilocal group algebras
• Quantum phase transition between symmetry enriched topological phases in tensor-network states

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