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:
- 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}
}
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.7.5.069
DOI: 10.21468/SciPostPhys.7.5.069
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 5 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry
journal, February 2019
- Jin, L.; Song, Z.
- Physical Review B, Vol. 99, Issue 8
Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
journal, February 2019
- Edvardsson, Elisabet; Kunst, Flore K.; Bergholtz, Emil J.
- Physical Review B, Vol. 99, Issue 8
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
journal, July 2018
- Kunst, Flore K.; Edvardsson, Elisabet; Budich, Jan Carl
- Physical Review Letters, Vol. 121, Issue 2
General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
journal, May 2012
- Qi, Xiao-Liang; Katsura, Hosho; Ludwig, Andreas W. W.
- Physical Review Letters, Vol. 108, Issue 19
Soliton excitations in polyacetylene
journal, August 1980
- Su, W. P.; Schrieffer, J. R.; Heeger, A. J.
- Physical Review B, Vol. 22, Issue 4
Non-Hermitian Quantum Dynamics of a Two-Level System and Models of Dissipative Environments
journal, October 2013
- Sergi, Alessandro; Zloshchastiev, Konstantin G.
- International Journal of Modern Physics B, Vol. 27, Issue 27
Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
journal, January 2017
- Xu, Yong; Wang, Sheng-Tao; Duan, L. -M.
- Physical Review Letters, Vol. 118, Issue 4
Real-space entanglement spectrum of quantum Hall states
journal, March 2012
- Sterdyniak, A.; Chandran, A.; Regnault, N.
- Physical Review B, Vol. 85, Issue 12
Photonic Topological Insulating Phase Induced Solely by Gain and Loss
journal, November 2018
- Takata, Kenta; Notomi, Masaya
- Physical Review Letters, Vol. 121, Issue 21
Non-commutative tools for topological insulators
journal, June 2010
- Prodan, Emil
- New Journal of Physics, Vol. 12, Issue 6
Topological Phases of Non-Hermitian Systems
journal, September 2018
- Gong, Zongping; Ashida, Yuto; Kawabata, Kohei
- Physical Review X, Vol. 8, Issue 3
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
journal, January 1997
- Altland, Alexander; Zirnbauer, Martin R.
- Physical Review B, Vol. 55, Issue 2
Non-Hermitian fractional quantum Hall states
journal, November 2019
- Yoshida, Tsuneya; Kudo, Koji; Hatsugai, Yasuhiro
- Scientific Reports, Vol. 9, Issue 1
Universality of Entropy Scaling in One Dimensional Gapless Models
journal, March 2004
- Korepin, V. E.
- Physical Review Letters, Vol. 92, Issue 9
Selective enhancement of topologically induced interface states in a dielectric resonator chain
journal, April 2015
- Poli, Charles; Bellec, Matthieu; Kuhl, Ulrich
- Nature Communications, Vol. 6, Issue 1
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
journal, July 2008
- Li, Hui; Haldane, F. D. M.
- Physical Review Letters, Vol. 101, Issue 1
Edge-Mode Lasing in 1D Topological Active Arrays
journal, March 2018
- Parto, Midya; Wittek, Steffen; Hodaei, Hossein
- Physical Review Letters, Vol. 120, Issue 11
Gaussian operator bases for correlated fermions
journal, December 2005
- Corney, J. F.; Drummond, P. D.
- Journal of Physics A: Mathematical and General, Vol. 39, Issue 2
Bulk-edge correspondence in entanglement spectra
journal, November 2011
- Chandran, Anushya; Hermanns, M.; Regnault, N.
- Physical Review B, Vol. 84, Issue 20
Topologically protected bound states in photonic parity–time-symmetric crystals
journal, December 2016
- Weimann, S.; Kremer, M.; Plotnik, Y.
- Nature Materials, Vol. 16, Issue 4
Non-Hermitian Majorana modes protect degenerate steady states
journal, August 2019
- Lieu, Simon
- Physical Review B, Vol. 100, Issue 8
Detecting Topological Order in a Ground State Wave Function
journal, March 2006
- Levin, Michael; Wen, Xiao-Gang
- Physical Review Letters, Vol. 96, Issue 11
Topological Entanglement Entropy
journal, March 2006
- Kitaev, Alexei; Preskill, John
- Physical Review Letters, Vol. 96, Issue 11
Classification of topological quantum matter with symmetries
journal, August 2016
- Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P.
- Reviews of Modern Physics, Vol. 88, Issue 3
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
journal, January 2017
- Leykam, Daniel; Bliokh, Konstantin Y.; Huang, Chunli
- Physical Review Letters, Vol. 118, Issue 4
Topological photonics
journal, October 2014
- Lu, Ling; Joannopoulos, John D.; Soljačić, Marin
- Nature Photonics, Vol. 8, Issue 11
Periodic table for topological insulators and superconductors
conference, January 2009
- Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail
- ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings
Building blocks of topological quantum chemistry: Elementary band representations
journal, January 2018
- Cano, Jennifer; Bradlyn, Barry; Wang, Zhijun
- Physical Review B, Vol. 97, Issue 3
Edge States and Topological Invariants of Non-Hermitian Systems
journal, August 2018
- Yao, Shunyu; Wang, Zhong
- Physical Review Letters, Vol. 121, Issue 8
Calculation of reduced density matrices from correlation functions
journal, March 2003
- Peschel, Ingo
- Journal of Physics A: Mathematical and General, Vol. 36, Issue 14
Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
journal, May 2018
- Yin, Chuanhao; Jiang, Hui; Li, Linhu
- Physical Review A, Vol. 97, Issue 5
Nonlocal Order in Gapless Systems: Entanglement Spectrum in Spin Chains
journal, September 2010
- Thomale, Ronny; Arovas, D. P.; Bernevig, B. Andrei
- Physical Review Letters, Vol. 105, Issue 11
Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
journal, May 2019
- Herviou, Loïc; Bardarson, Jens H.; Regnault, Nicolas
- Physical Review A, Vol. 99, Issue 5
Topological Transition in a Non-Hermitian Quantum Walk
journal, February 2009
- Rudner, M. S.; Levitov, L. S.
- Physical Review Letters, Vol. 102, Issue 6
Topological invariance and global Berry phase in non-Hermitian systems
journal, January 2013
- Liang, Shi-Dong; Huang, Guang-Yao
- Physical Review A, Vol. 87, Issue 1
Monte Carlo wave-function method in quantum optics
journal, January 1993
- Mølmer, Klaus; Castin, Yvan; Dalibard, Jean
- Journal of the Optical Society of America B, Vol. 10, Issue 3
Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010
- Ryu, Shinsei; Schnyder, Andreas P.; Furusaki, Akira
- New Journal of Physics, Vol. 12, Issue 6
Non-Bloch Band Theory of Non-Hermitian Systems
journal, August 2019
- Yokomizo, Kazuki; Murakami, Shuichi
- Physical Review Letters, Vol. 123, Issue 6
Monte Carlo simulation of the atomic master equation for spontaneous emission
journal, April 1992
- Dum, R.; Zoller, P.; Ritsch, H.
- Physical Review A, Vol. 45, Issue 7
A classification of 2D random Dirac fermions
journal, March 2002
- Bernard, Denis; LeClair, André
- Journal of Physics A: Mathematical and General, Vol. 35, Issue 11
Anatomy of skin modes and topology in non-Hermitian systems
journal, May 2019
- Lee, Ching Hua; Thomale, Ronny
- Physical Review B, Vol. 99, Issue 20
Symmetry and Topology in Non-Hermitian Physics
journal, October 2019
- Kawabata, Kohei; Shiozaki, Ken; Ueda, Masahito
- Physical Review X, Vol. 9, Issue 4
Random matrices beyond the Cartan classification
journal, January 2008
- Magnea, Ulrika
- Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 4
Topological insulators with inversion symmetry
journal, July 2007
- Fu, Liang; Kane, C. L.
- Physical Review B, Vol. 76, Issue 4
Topological classification of non-Hermitian systems with reflection symmetry
journal, March 2019
- Liu, Chun-Hui; Jiang, Hui; Chen, Shu
- Physical Review B, Vol. 99, Issue 12
Topological Order and the Quantum Spin Hall Effect
journal, September 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 14, Article No. 146802
Topological hybrid silicon microlasers
journal, March 2018
- Zhao, Han; Miao, Pei; Teimourpour, Mohammad H.
- Nature Communications, Vol. 9, Issue 1
Colloquium: Topological insulators
journal, November 2010
- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
Non-Hermitian Gauged Topological Laser Arrays
journal, May 2018
- Longhi, Stefano
- Annalen der Physik, Vol. 530, Issue 7
Non-Hermitian Chern Bands
journal, September 2018
- Yao, Shunyu; Song, Fei; Wang, Zhong
- Physical Review Letters, Vol. 121, Issue 13
Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
journal, January 2018
- Lieu, Simon
- Physical Review B, Vol. 97, Issue 4
Topological Band Theory for Non-Hermitian Hamiltonians
journal, April 2018
- Shen, Huitao; Zhen, Bo; Fu, Liang
- Physical Review Letters, Vol. 120, Issue 14
Wave-function approach to dissipative processes in quantum optics
journal, February 1992
- Dalibard, Jean; Castin, Yvan; Mølmer, Klaus
- Physical Review Letters, Vol. 68, Issue 5
Topological states of non-Hermitian systems
journal, October 2018
- Martinez Alvarez, V. M.; Barrios Vargas, J. E.; Berdakin, M.
- The European Physical Journal Special Topics, Vol. 227, Issue 12
Topological quantum chemistry
journal, July 2017
- Bradlyn, Barry; Elcoro, L.; Cano, Jennifer
- Nature, Vol. 547, Issue 7663
Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov–de Gennes equation
journal, September 2018
- Lieu, Simon
- Physical Review B, Vol. 98, Issue 11
Topological Insulators in Three Dimensions
journal, March 2007
- Fu, Liang; Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 98, Issue 10, Article No. 106803
Classification of topological insulators and superconductors in three spatial dimensions
journal, November 2008
- Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira
- Physical Review B, Vol. 78, Issue 19
Entanglement in Quantum Critical Phenomena
journal, June 2003
- Vidal, G.; Latorre, J. I.; Rico, E.
- Physical Review Letters, Vol. 90, Issue 22
Geometric proof of the equality between entanglement and edge spectra
journal, July 2012
- Swingle, Brian; Senthil, T.
- Physical Review B, Vol. 86, Issue 4
Anomalous Light Scattering by Topological PT-symmetric Particle Arrays
journal, December 2016
- Ling, C. W.; Choi, Ka Hei; Mok, T. C.
- Scientific Reports, Vol. 6, Issue 1
Topological Classification of Crystalline Insulators through Band Structure Combinatorics
journal, December 2017
- Kruthoff, Jorrit; de Boer, Jan; van Wezel, Jasper
- Physical Review X, Vol. 7, Issue 4
Why does bulk boundary correspondence fail in some non-hermitian topological models
journal, March 2018
- Xiong, Ye
- Journal of Physics Communications, Vol. 2, Issue 3
Trace index and spectral flow in the entanglement spectrum of topological insulators
journal, November 2011
- Alexandradinata, A.; Hughes, Taylor L.; Bernevig, B. Andrei
- Physical Review B, Vol. 84, Issue 19
Topological dynamics and excitations in lasers and condensates with saturable gain or loss
journal, January 2018
- Malzard, Simon; Cancellieri, Emiliano; Schomerus, Henning
- Optics Express, Vol. 26, Issue 17
Biorthogonal quantum mechanics
journal, December 2013
- Brody, Dorje C.
- Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 3
Periodic table for topological bands with non-Hermitian symmetries
journal, June 2019
- Zhou, Hengyun; Lee, Jong Yeon
- Physical Review B, Vol. 99, Issue 23
Entanglement Spectrum of Topological Insulators and Superconductors
journal, April 2010
- Fidkowski, Lukasz
- Physical Review Letters, Vol. 104, Issue 13
Entanglement entropy and quantum field theory
journal, June 2004
- Calabrese, Pasquale; Cardy, John
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2004, Issue 06
Entanglement spectrum of a topological phase in one dimension
journal, February 2010
- Pollmann, Frank; Turner, Ari M.; Berg, Erez
- Physical Review B, Vol. 81, Issue 6
Entanglement Spectrum of a Disordered Topological Chern Insulator
journal, September 2010
- Prodan, Emil; Hughes, Taylor L.; Bernevig, B. Andrei
- Physical Review Letters, Vol. 105, Issue 11
Topologically protected midgap states in complex photonic lattices
journal, January 2013
- Schomerus, Henning
- Optics Letters, Vol. 38, Issue 11
Anomalous Edge State in a Non-Hermitian Lattice
journal, April 2016
- Lee, Tony E.
- Physical Review Letters, Vol. 116, Issue 13
Heralded Magnetism in Non-Hermitian Atomic Systems
journal, October 2014
- Lee, Tony E.; Chan, Ching-Kit
- Physical Review X, Vol. 4, Issue 4
Edge states and topological phases in non-Hermitian systems
journal, November 2011
- Esaki, Kenta; Sato, Masatoshi; Hasebe, Kazuki
- Physical Review B, Vol. 84, Issue 20
Non-Hermitian perspective of the band structure in heavy-fermion systems
journal, July 2018
- Yoshida, Tsuneya; Peters, Robert; Kawakami, Norio
- Physical Review B, Vol. 98, Issue 3
Entanglement and inversion symmetry in topological insulators
journal, December 2010
- Turner, Ari M.; Zhang, Yi; Vishwanath, Ashvin
- Physical Review B, Vol. 82, Issue 24
Mapping topological order in coordinate space
journal, December 2011
- Bianco, Raffaello; Resta, Raffaele
- Physical Review B, Vol. 84, Issue 24