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:
-
- Royal Institute of Technology (KTH)
- École Normale Supérieure, Princeton University
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1576038
- Alternate Identifier(s):
- OSTI ID: 1802881
- 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
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics
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. https://doi.org/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. https://doi.org/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}
}
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https://doi.org/10.21468/SciPostPhys.7.5.069
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