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Title: Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models

Abstract

We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.

Authors:
 [1];  [2];  [1]
  1. Royal Institute of Technology (KTH)
  2. École Normale Supérieure, Princeton University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1576038
Grant/Contract Number:  
SC0016239
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 5; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Herviou, Loïc, Regnault, Nicolas, and Bardarson, Jens H. Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models. Netherlands: N. p., 2019. Web. doi:10.21468/SciPostPhys.7.5.069.
Herviou, Loïc, Regnault, Nicolas, & Bardarson, Jens H. Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models. Netherlands. doi:10.21468/SciPostPhys.7.5.069.
Herviou, Loïc, Regnault, Nicolas, and Bardarson, Jens H. Thu . "Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models". Netherlands. doi:10.21468/SciPostPhys.7.5.069.
@article{osti_1576038,
title = {Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models},
author = {Herviou, Loïc and Regnault, Nicolas and Bardarson, Jens H.},
abstractNote = {We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.},
doi = {10.21468/SciPostPhys.7.5.069},
journal = {SciPost Physics Proceedings},
number = 5,
volume = 7,
place = {Netherlands},
year = {2019},
month = {11}
}

Journal Article:
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DOI: 10.21468/SciPostPhys.7.5.069

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