Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

Murciano, Sara; Di Giulio, Giuseppe; Calabrese, Pasquale

doi:10.21468/SciPostPhys.8.3.046

SciPost Physics

Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

Sara Murciano, Giuseppe Di Giulio, Pasquale Calabrese

SciPost Phys. 8, 046 (2020) · published 26 March 2020

doi: 10.21468/SciPostPhys.8.3.046
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Abstract

We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.8.3.046
TI  - Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
PY  - 2020/03/26
UR  - https://www.scipost.org/SciPostPhys.8.3.046
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 8
IS  - 3
SP  - 046
A1  - Murciano, Sara
AU  - Di Giulio, Giuseppe
AU  - Calabrese, Pasquale
AB  - We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.
ER  -

@Article{10.21468/SciPostPhys.8.3.046,
	title={{Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach}},
	author={Sara Murciano and Giuseppe Di Giulio and Pasquale Calabrese},
	journal={SciPost Phys.},
	volume={8},
	pages={046},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.8.3.046},
	url={https://scipost.org/10.21468/SciPostPhys.8.3.046},
}

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Entanglement Transfer matrix XXZ model

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Funder for the research work leading to this publication

European Research Council [ERC]