Entanglement properties of Floquet-Chern insulators

Yates, Daniel J.; Lemonik, Yonah; Mitra, Aditi

doi:10.1103/physrevb.94.205422

Title: Entanglement properties of Floquet-Chern insulators

Journal Article · Wed Nov 16 00:00:00 EST 2016 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.94.205422· OSTI ID:1535801

Yates, Daniel J. ^[1]; Lemonik, Yonah ^[1]; Mitra, Aditi ^[1]

New York Univ. (NYU), NY (United States)

Results are presented for the entanglement entropy and spectrum of half-filled graphene following the switch on of a circularly polarized laser. The laser parameters are chosen to correspond to several different Floquet-Chern insulator phases. The entanglement properties of the unitarily evolved wave functions are compared with the state where one of the Floquet bands is completely occupied. The true states show a volume law for the entanglement, whereas the Floquet states show an area law. Qualitative differences are found in the entanglement properties of the off-resonant and on-resonant laser. Edge states are found in the entanglement spectrum corresponding to certain physical edge states expected in a Chern insulator. However, some edge states that would be expected from the Floquet band structure are missing from the entanglement spectrum. An analytic theory is developed for the long-time structure of the entanglement spectrum. Finally, it is argued that only edge states corresponding to off-resonant processes appear in the entanglement spectrum.

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Research Organization:: New York Univ. (NYU), NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0010821

OSTI ID:: 1535801

Alternate ID(s):: OSTI ID: 1332387

Journal Information:: Physical Review B, Vol. 94, Issue 20; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (43)

The density-matrix renormalization group in the age of matrix product states Schollwöck, Ulrich Annals of Physics, Vol. 326, Issue 1 https://doi.org/10.1016/j.aop.2010.09.012	journal	January 2011
Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems Rudner, Mark S.; Lindner, Netanel H.; Berg, Erez Physical Review X, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevX.3.031005	journal	July 2013
Effective Theory of Floquet Topological Transitions Kundu, Arijit; Fertig, H. A.; Seradjeh, Babak Physical Review Letters, Vol. 113, Issue 23 https://doi.org/10.1103/PhysRevLett.113.236803	journal	December 2014
Colloquium : Area laws for the entanglement entropy Eisert, J.; Cramer, M.; Plenio, M. B. Reviews of Modern Physics, Vol. 82, Issue 1 https://doi.org/10.1103/RevModPhys.82.277	journal	February 2010
Reduced density matrices and entanglement entropy in free lattice models Peschel, Ingo; Eisler, Viktor Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 50 https://doi.org/10.1088/1751-8113/42/50/504003	journal	December 2009
Floquet topological insulator in semiconductor quantum wells Lindner, Netanel H.; Refael, Gil; Galitski, Victor Nature Physics, Vol. 7, Issue 6 https://doi.org/10.1038/nphys1926	journal	March 2011
Photonic Floquet topological insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan Nature, Vol. 496, Issue 7444 https://doi.org/10.1038/nature12066	journal	April 2013
Photovoltaic Hall effect in graphene Oka, Takashi; Aoki, Hideo Physical Review B, Vol. 79, Issue 8 https://doi.org/10.1103/PhysRevB.79.081406	journal	February 2009
Topological Rényi Entropy after a Quantum Quench Halász, Gábor B.; Hamma, Alioscia Physical Review Letters, Vol. 110, Issue 17 https://doi.org/10.1103/PhysRevLett.110.170605	journal	April 2013
Optical Hall conductivity of a Floquet topological insulator Dehghani, Hossein; Mitra, Aditi Physical Review B, Vol. 92, Issue 16 https://doi.org/10.1103/PhysRevB.92.165111	journal	October 2015
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States Li, Hui; Haldane, F. D. M. Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevLett.101.010504	journal	July 2008
Many-Body Localization in Periodically Driven Systems Ponte, Pedro; Papić, Z.; Huveneers, François Physical Review Letters, Vol. 114, Issue 14 https://doi.org/10.1103/PhysRevLett.114.140401	journal	April 2015
Entanglement properties of the critical quench of $O (N)$ bosons Lemonik, Yonah; Mitra, Aditi Physical Review B, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevB.94.024306	journal	July 2016
Photoinduced Transition between Conventional and Topological Insulators in Two-Dimensional Electronic Systems Inoue, Jun-ichi; Tanaka, Akihiro Physical Review Letters, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevLett.105.017401	journal	June 2010
Numerical time propagation of quantum systems in radiation fields Alvermann, A.; Fehske, H.; Littlewood, P. B. New Journal of Physics, Vol. 14, Issue 10 https://doi.org/10.1088/1367-2630/14/10/105008	journal	October 2012
Detecting Topological Order in a Ground State Wave Function Levin, Michael; Wen, Xiao-Gang Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.110405	journal	March 2006
Out-of-equilibrium electrons and the Hall conductance of a Floquet topological insulator Dehghani, Hossein; Oka, Takashi; Mitra, Aditi Physical Review B, Vol. 91, Issue 15 https://doi.org/10.1103/PhysRevB.91.155422	journal	April 2015
Experimental realization of the topological Haldane model with ultracold fermions Jotzu, Gregor; Messer, Michael; Desbuquois, Rémi Nature, Vol. 515, Issue 7526 https://doi.org/10.1038/nature13915	journal	November 2014
Topological Entanglement Entropy Kitaev, Alexei; Preskill, John Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.110404	journal	March 2006
Quantum annealing and nonequilibrium dynamics of Floquet Chern insulators Privitera, Lorenzo; Santoro, Giuseppe E. Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/PhysRevB.93.241406	journal	June 2016
Dynamical preparation of Floquet Chern insulators D’Alessio, Luca; Rigol, Marcos Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9336	journal	October 2015
Universal terms for the entanglement entropy in dimensions Casini, H.; Huerta, M. Nuclear Physics B, Vol. 764, Issue 3 https://doi.org/10.1016/j.nuclphysb.2006.12.012	journal	March 2007
Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator Dehghani, Hossein; Mitra, Aditi Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.205437	journal	May 2016
Multiterminal Conductance of a Floquet Topological Insulator Foa Torres, L. E. F.; Perez-Piskunow, P. M.; Balseiro, C. A. Physical Review Letters, Vol. 113, Issue 26 https://doi.org/10.1103/PhysRevLett.113.266801	journal	December 2014
Many-Body Localization Implies that Eigenvectors are Matrix-Product States Friesdorf, M.; Werner, A. H.; Brown, W. Physical Review Letters, Vol. 114, Issue 17 https://doi.org/10.1103/PhysRevLett.114.170505	journal	May 2015
Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels Kitagawa, Takuya; Oka, Takashi; Brataas, Arne Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235108	journal	December 2011
Entanglement Spectrum of Topological Insulators and Superconductors Fidkowski, Lukasz Physical Review Letters, Vol. 104, Issue 13 https://doi.org/10.1103/PhysRevLett.104.130502	journal	April 2010
Quantized Hall conductivity in two dimensions Laughlin, R. B. Physical Review B, Vol. 23, Issue 10 https://doi.org/10.1103/PhysRevB.23.5632	journal	May 1981
Long-time Behavior of Isolated Periodically Driven Interacting Lattice Systems D’Alessio, Luca; Rigol, Marcos Physical Review X, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevX.4.041048	journal	December 2014
Entanglement entropy in the $O (N)$ model Metlitski, Max A.; Fuertes, Carlos A.; Sachdev, Subir Physical Review B, Vol. 80, Issue 11 https://doi.org/10.1103/PhysRevB.80.115122	journal	September 2009
Dissipative Floquet topological systems Dehghani, Hossein; Oka, Takashi; Mitra, Aditi Physical Review B, Vol. 90, Issue 19 https://doi.org/10.1103/PhysRevB.90.195429	journal	November 2014
Fate of Many-Body Localization Under Periodic Driving Lazarides, Achilleas; Das, Arnab; Moessner, Roderich Physical Review Letters, Vol. 115, Issue 3 https://doi.org/10.1103/PhysRevLett.115.030402	journal	July 2015
Photonic Floquet topological insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan SPIE NanoScience + Engineering, SPIE Proceedings https://doi.org/10.1117/12.2023842	conference	September 2013
Photovoltaic Hall effect in graphene Oka, Takashi; Aoki, Hideo arXiv https://doi.org/10.48550/arxiv.0807.4767	text	January 2008
The density-matrix renormalization group in the age of matrix product states Schollwoeck, Ulrich arXiv https://doi.org/10.48550/arxiv.1008.3477	text	January 2010
Numerical time propagation of quantum systems in radiation fields Alvermann, A.; Fehske, H.; Littlewood, P. B. arXiv https://doi.org/10.48550/arxiv.1205.1379	text	January 2012
Photonic Floquet Topological Insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan arXiv https://doi.org/10.48550/arxiv.1212.3146	text	January 2012
Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems Rudner, Mark S.; Lindner, Netanel H.; Berg, Erez arXiv https://doi.org/10.48550/arxiv.1212.3324	text	January 2012
Effective Theory of Floquet Topological Transitions Kundu, Arijit; Fertig, H. A.; Seradjeh, Babak arXiv https://doi.org/10.48550/arxiv.1406.1490	text	January 2014
Fate of many-body localization under periodic driving Lazarides, Achilleas; Das, Arnab; Moessner, Roderich arXiv https://doi.org/10.48550/arxiv.1410.3455	text	January 2014
Optical Hall conductivity of a Floquet Topological Insulator Dehghani, Hossein; Mitra, Aditi arXiv https://doi.org/10.48550/arxiv.1506.08687	text	January 2015
Quantum annealing and non-equilibrium dynamics of Floquet Chern insulators Privitera, Lorenzo; Santoro, Giuseppe E. arXiv https://doi.org/10.48550/arxiv.1508.01883	text	January 2015
Entanglement properties of the critical quench of O(N) bosons Lemonik, Yonah; Mitra, Aditi arXiv https://doi.org/10.48550/arxiv.1512.02749	text	January 2015

Cited By (3)

Topological marker currents in Chern insulators Caio, M. D.; Möller, G.; Cooper, N. R. Nature Physics, Vol. 15, Issue 3 https://doi.org/10.1038/s41567-018-0390-7	journal	January 2019
Topological Entanglement-Spectrum Crossing in Quench Dynamics Gong, Zongping; Ueda, Masahito Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/physrevlett.121.250601	journal	December 2018
Topological Entanglement-Spectrum Crossing in Quench Dynamics Gong, Zongping; Ueda, Masahito arXiv https://doi.org/10.48550/arxiv.1710.05289	text	January 2017

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