Entanglement of Gauge Theories: from the Toric Code to the $\mathbb{Z}_2$ Lattice Gauge Higgs Model

• URL: http://arxiv.org/abs/2311.16235v1
• Date: Mon, 27 Nov 2023 19:00:02 GMT
• Title: Entanglement of Gauge Theories: from the Toric Code to the $\mathbb{Z}_2$ Lattice Gauge Higgs Model
• Authors: Wen-Tao Xu, Michael Knap, Frank Pollmann
• Abstract summary: We show that mapping the toric code (TC) model to the Higgs ($mathbbZ$ GH) model has a non-trivial effect on the entanglement structure. We derive a quantum channel that allows us to obtain the reduced density matrix of the $mathbbZ$ GH model from the one of the TC model.
• Score: 2.570568710751949
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The toric code (TC) model subjected to a magnetic field can be mapped to the $\mathbb{Z}_2$ lattice gauge Higgs ($\mathbb{Z}_2$ GH) model. Although this isometric mapping preserves the bulk energy spectrum, here, we show that it has a non-trivial effect on the entanglement structure. We derive a quantum channel that allows us to obtain the reduced density matrix of the $\mathbb{Z}_2$ GH model from the one of the TC model. We then contrast the ground state entanglement spectra (ES) of the two models. Analyzing the role of the electric-magnetic duality, we show that while the ES of the TC model is enriched by the duality, the ES of the $\mathbb{Z}_2$ GH model is in fact not. This thus represents an example where the bulk-boundary correspondence fails. Moreover, the quantum channel allows us to investigate the entanglement distillation of the $\mathbb{Z}_2$ GH model from the TC model.

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