Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

Micallo, Tommaso; Vitale, Vittorio; Dalmonte, Marcello; Fromholz, Pierre

doi:10.21468/SciPostPhysCore.3.2.012

SciPost Physics Core

Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

Tommaso Micallo, Vittorio Vitale, Marcello Dalmonte, Pierre Fromholz

SciPost Phys. Core 3, 012 (2020) · published 1 December 2020

doi: 10.21468/SciPostPhysCore.3.2.012
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Abstract

We study the disconnected entanglement entropy, $S^D$, of the Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions, and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that $S^D$ behaves as a topological invariant, i.e., it is quantized to either $0$ or $2 \log (2)$ in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, $S^D$ displays a system-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of $S^D$, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.3.2.012
TI  - Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model
PY  - 2020/12/01
UR  - https://scipost.org/SciPostPhysCore.3.2.012
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 3
IS  - 2
SP  - 012
A1  - Micallo, Tommaso
AU  - Vitale, Vittorio
AU  - Dalmonte, Marcello
AU  - Fromholz, Pierre
AB  - We study the disconnected entanglement entropy, $S^D$, of the Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions, and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that $S^D$ behaves as a topological invariant, i.e., it is quantized to either $0$ or $2 \log (2)$ in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, $S^D$ displays a system-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of $S^D$, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants.
ER  -

@Article{10.21468/SciPostPhysCore.3.2.012,
	title={{Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model}},
	author={Tommaso Micallo and Vittorio Vitale and Marcello Dalmonte and Pierre Fromholz},
	journal={SciPost Phys. Core},
	volume={3},
	pages={012},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.3.2.012},
	url={https://scipost.org/10.21468/SciPostPhysCore.3.2.012},
}

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Authors / Affiliations: mappings to Contributors and Organizations

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¹ ² ³ ⁴ Tommaso Micallo,
¹ ² Vittorio Vitale,
¹ ² Marcello Dalmonte,
¹ ² Pierre Fromholz

Funders for the research work leading to this publication

European Research Council [ERC]
Horizon 2020 (through Organization: European Commission [EC])