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

Abstract

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.

Authors:

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

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

Publication Date:: Wed Nov 16 00:00:00 EST 2016

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

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

OSTI Identifier:: 1535801

Alternate Identifier(s):: OSTI ID: 1332387

Grant/Contract Number:: SC0010821

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 94; Journal Issue: 20; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; materials science; physics; conformation & topology; light-matter interaction; quantum entanglement; graphene; topological insulators

Citation Formats


                    Yates, Daniel J., Lemonik, Yonah, and Mitra, Aditi. Entanglement properties of Floquet-Chern insulators.  United States: N. p., 2016. 
Web.  doi:10.1103/physrevb.94.205422.

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                    Yates, Daniel J., Lemonik, Yonah, & Mitra, Aditi. Entanglement properties of Floquet-Chern insulators.  United States.  https://doi.org/10.1103/physrevb.94.205422

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                    Yates, Daniel J., Lemonik, Yonah, and Mitra, Aditi. Wed .  
"Entanglement properties of Floquet-Chern insulators".  United States.  https://doi.org/10.1103/physrevb.94.205422.  https://www.osti.gov/servlets/purl/1535801.

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@article{osti_1535801,

  title        = {Entanglement properties of Floquet-Chern insulators},

  author       = {Yates, Daniel J. and Lemonik, Yonah and Mitra, Aditi},

  abstractNote = {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.},

  doi          = {10.1103/physrevb.94.205422},

  journal      = {Physical Review B},

  number       = 20,

  volume       = 94,

  place        = {United States},

  year         = {Wed Nov 16 00:00:00 EST 2016},

  month        = {Wed Nov 16 00:00:00 EST 2016}

}

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Topological marker currents in Chern insulators
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Title: Entanglement properties of Floquet-Chern insulators

Abstract

Citation Formats

The density-matrix renormalization group in the age of matrix product states journal, January 2011

Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems journal, July 2013

Effective Theory of Floquet Topological Transitions journal, December 2014

Colloquium : Area laws for the entanglement entropy journal, February 2010

Reduced density matrices and entanglement entropy in free lattice models journal, December 2009

Floquet topological insulator in semiconductor quantum wells journal, March 2011

Photonic Floquet topological insulators journal, April 2013

Photovoltaic Hall effect in graphene journal, February 2009

Topological Rényi Entropy after a Quantum Quench journal, April 2013

Optical Hall conductivity of a Floquet topological insulator journal, October 2015

Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States journal, July 2008

Many-Body Localization in Periodically Driven Systems journal, April 2015

Entanglement properties of the critical quench of O ( N ) bosons journal, July 2016

Photoinduced Transition between Conventional and Topological Insulators in Two-Dimensional Electronic Systems journal, June 2010

Numerical time propagation of quantum systems in radiation fields journal, October 2012

Detecting Topological Order in a Ground State Wave Function journal, March 2006

Out-of-equilibrium electrons and the Hall conductance of a Floquet topological insulator journal, April 2015

Experimental realization of the topological Haldane model with ultracold fermions journal, November 2014

Topological Entanglement Entropy journal, March 2006

Quantum annealing and nonequilibrium dynamics of Floquet Chern insulators journal, June 2016

Dynamical preparation of Floquet Chern insulators journal, October 2015

Universal terms for the entanglement entropy in dimensions journal, March 2007

Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator journal, May 2016

Multiterminal Conductance of a Floquet Topological Insulator journal, December 2014

Many-Body Localization Implies that Eigenvectors are Matrix-Product States journal, May 2015

Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels journal, December 2011

Entanglement Spectrum of Topological Insulators and Superconductors journal, April 2010

Quantized Hall conductivity in two dimensions journal, May 1981

Long-time Behavior of Isolated Periodically Driven Interacting Lattice Systems journal, December 2014

Entanglement entropy in the O ( N ) model journal, September 2009

Dissipative Floquet topological systems journal, November 2014

Fate of Many-Body Localization Under Periodic Driving journal, July 2015

Photonic Floquet topological insulators conference, September 2013

Photovoltaic Hall effect in graphene text, January 2008

The density-matrix renormalization group in the age of matrix product states text, January 2010

Numerical time propagation of quantum systems in radiation fields text, January 2012

Photonic Floquet Topological Insulators text, January 2012

Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems text, January 2012

Effective Theory of Floquet Topological Transitions text, January 2014

Fate of many-body localization under periodic driving text, January 2014

Optical Hall conductivity of a Floquet Topological Insulator text, January 2015

Quantum annealing and non-equilibrium dynamics of Floquet Chern insulators text, January 2015

Entanglement properties of the critical quench of O(N) bosons text, January 2015

Topological marker currents in Chern insulators journal, January 2019

Topological Entanglement-Spectrum Crossing in Quench Dynamics journal, December 2018

Topological Entanglement-Spectrum Crossing in Quench Dynamics text, January 2017

The density-matrix renormalization group in the age of matrix product states
journal, January 2011

Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems
journal, July 2013

Effective Theory of Floquet Topological Transitions
journal, December 2014

Colloquium : Area laws for the entanglement entropy
journal, February 2010

Reduced density matrices and entanglement entropy in free lattice models
journal, December 2009

Floquet topological insulator in semiconductor quantum wells
journal, March 2011

Photonic Floquet topological insulators
journal, April 2013

Photovoltaic Hall effect in graphene
journal, February 2009

Topological Rényi Entropy after a Quantum Quench
journal, April 2013

Optical Hall conductivity of a Floquet topological insulator
journal, October 2015

Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
journal, July 2008

Many-Body Localization in Periodically Driven Systems
journal, April 2015

Entanglement properties of the critical quench of $O (N)$ bosons
journal, July 2016

Photoinduced Transition between Conventional and Topological Insulators in Two-Dimensional Electronic Systems
journal, June 2010

Numerical time propagation of quantum systems in radiation fields
journal, October 2012

Detecting Topological Order in a Ground State Wave Function
journal, March 2006

Out-of-equilibrium electrons and the Hall conductance of a Floquet topological insulator
journal, April 2015

Experimental realization of the topological Haldane model with ultracold fermions
journal, November 2014

Topological Entanglement Entropy
journal, March 2006

Quantum annealing and nonequilibrium dynamics of Floquet Chern insulators
journal, June 2016

Dynamical preparation of Floquet Chern insulators
journal, October 2015

Universal terms for the entanglement entropy in dimensions
journal, March 2007

Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator
journal, May 2016

Multiterminal Conductance of a Floquet Topological Insulator
journal, December 2014

Many-Body Localization Implies that Eigenvectors are Matrix-Product States
journal, May 2015

Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels
journal, December 2011

Entanglement Spectrum of Topological Insulators and Superconductors
journal, April 2010

Quantized Hall conductivity in two dimensions
journal, May 1981

Long-time Behavior of Isolated Periodically Driven Interacting Lattice Systems
journal, December 2014

Entanglement entropy in the $O (N)$ model
journal, September 2009

Dissipative Floquet topological systems
journal, November 2014

Fate of Many-Body Localization Under Periodic Driving
journal, July 2015

Photonic Floquet topological insulators
conference, September 2013

Photovoltaic Hall effect in graphene
text, January 2008

The density-matrix renormalization group in the age of matrix product states
text, January 2010

Numerical time propagation of quantum systems in radiation fields
text, January 2012

Photonic Floquet Topological Insulators
text, January 2012

Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems
text, January 2012

Effective Theory of Floquet Topological Transitions
text, January 2014

Fate of many-body localization under periodic driving
text, January 2014

Optical Hall conductivity of a Floquet Topological Insulator
text, January 2015

Quantum annealing and non-equilibrium dynamics of Floquet Chern insulators
text, January 2015

Entanglement properties of the critical quench of O(N) bosons
text, January 2015

Topological marker currents in Chern insulators
journal, January 2019

Topological Entanglement-Spectrum Crossing in Quench Dynamics
journal, December 2018

Topological Entanglement-Spectrum Crossing in Quench Dynamics
text, January 2017