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Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0003-4220-8785
Princeton Univ, Joseph Henry Labs, Princeton, NJ 08544 USA.;Princeton Univ, Dept Phys, Princeton, NJ 08544 USA.;Univ Paris Diderot, Sorbonne Paris Cite, Sorbonne Univ, Lab Phys Ecole Normale Super,ENS,Univ PSL,CNRS, Paris, France..
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0003-3328-8525
2019 (English)In: SciPost Physics, ISSN 2542-4653, Vol. 7, no 5, article id 069Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SciPost Foundation , 2019. Vol. 7, no 5, article id 069
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Physical Sciences
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URN: urn:nbn:se:kth:diva-266200DOI: 10.21468/SciPostPhys.7.5.069ISI: 000500735700012OAI: oai:DiVA.org:kth-266200DiVA, id: diva2:1383487
Note

QC 20200108

Available from: 2020-01-08 Created: 2020-01-08 Last updated: 2020-01-08Bibliographically approved

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Herviou, LoicBardarson, Jens H.

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