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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