Universality of quantum information in chaotic CFTs

Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong

doi:10.1007/jhep03(2018)070

Title: Universality of quantum information in chaotic CFTs

Abstract

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

Authors:

Lashkari, Nima ^[1]; Dymarsky, Anatoly ^[2]; Liu, Hong ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Univ. of Kentucky, Lexington, KY (United States); Skolkovo Inst. of Science and Technology, Moscow, (Russia)

Publication Date:: Mon Mar 12 00:00:00 EDT 2018

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1498701

Grant/Contract Number:: SC0012567

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 3; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Integrable Hierarchies; Thermal Field Theory

Citation Formats


                    Lashkari, Nima, Dymarsky, Anatoly, and Liu, Hong. Universality of quantum information in chaotic CFTs.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep03(2018)070.

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                    Lashkari, Nima, Dymarsky, Anatoly, & Liu, Hong. Universality of quantum information in chaotic CFTs.  United States.  https://doi.org/10.1007/jhep03(2018)070

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                    Lashkari, Nima, Dymarsky, Anatoly, and Liu, Hong. Mon .  
"Universality of quantum information in chaotic CFTs".  United States.  https://doi.org/10.1007/jhep03(2018)070.  https://www.osti.gov/servlets/purl/1498701.

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@article{osti_1498701,

  title        = {Universality of quantum information in chaotic CFTs},

  author       = {Lashkari, Nima and Dymarsky, Anatoly and Liu, Hong},

  abstractNote = {We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.},

  doi          = {10.1007/jhep03(2018)070},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 3,

  volume       = 2018,

  place        = {United States},

  year         = {Mon Mar 12 00:00:00 EDT 2018},

  month        = {Mon Mar 12 00:00:00 EDT 2018}

}

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Title: Universality of quantum information in chaotic CFTs

Abstract

Citation Formats

Virasoro conformal blocks and thermality from classical background fields journal, November 2015

Thermalization and its mechanism for generic isolated quantum systems journal, April 2008

A general transformation formula for conformal fields journal, April 1994

Eikonalization of conformal blocks journal, September 2015

Eigenstate thermalization hypothesis in conformal field theory journal, March 2018

Thermality of eigenstates in conformal field theories journal, August 2017

Relative entropy and holography journal, August 2013

Local quantum physics journal, December 1996

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis journal, December 2017

Local Quantum Physics book, January 1992

Remarks on thermalization in 2D CFT journal, December 2016

Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT journal, August 2017

Local Quantum Physics book, January 1996

Bulk emergence and the RG flow of entanglement entropy journal, May 2015

Implications of Conformal Invariance in Field Theories for General Dimensions journal, May 1994

Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz journal, April 1996

Recursive representation of the torus 1-point conformal block journal, January 2010

Thermal fluctuations in quantized chaotic systems journal, February 1996

Holographic entanglement entropy from 2d CFT: heavy states and local quenches journal, February 2015

Recursive representation of the torus 1-point conformal block text, January 2009

Bulk Emergence and the RG Flow of Entanglement Entropy text, January 2014

Virasoro Conformal Blocks and Thermality from Classical Background Fields text, January 2015

Eikonalization of Conformal Blocks text, January 2015

Eigenstate Thermalization Hypothesis in Conformal Field Theory text, January 2016

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis text, January 2017

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz text, January 1994

Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation journal, December 1997

Thermal correlation functions of KdV charges in 2D CFT journal, February 2019

Generalized Gibbs ensemble and the statistics of KdV charges in 2D CFT journal, March 2019

Entanglement entropy in (1+1)D CFTs with multiple local excitations journal, May 2018

Generalized Gibbs Ensemble and the Statistics of KdV Charges in 2D CFT text, January 2018

Exact generalized partition function of 2D CFTs at large central charge journal, May 2019

Rényi entropy at large energy density in 2D CFT journal, August 2019

The bulk-to-boundary propagator in black hole microstate backgrounds journal, June 2019

Eigenstate thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach journal, October 2019

Thermal Correlation Functions of KdV Charges in 2D CFT text, January 2018

Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit journal, January 2019

Note on ETH of descendant states in 2D CFT journal, January 2019

Probing thermality beyond the diagonal text, January 2018

Entanglement entropy in (1+1)D CFTs with multiple local excitations text, January 2018

The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds preprint, January 2018

Thermal Correlation Functions of KdV Charges in 2D CFT text, January 2018

Exact generalized partition function of 2D CFTs at large central charge text, January 2018

Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit journal, January 2019

Zero modes of local operators in 2d CFT on a cylinder journal, July 2020

Virasoro conformal blocks and thermality from classical background fields
journal, November 2015

Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

A general transformation formula for conformal fields
journal, April 1994

Eikonalization of conformal blocks
journal, September 2015

Eigenstate thermalization hypothesis in conformal field theory
journal, March 2018

Thermality of eigenstates in conformal field theories
journal, August 2017

Relative entropy and holography
journal, August 2013

Local quantum physics
journal, December 1996

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
journal, December 2017

Local Quantum Physics
book, January 1992

Remarks on thermalization in 2D CFT
journal, December 2016

Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
journal, August 2017

Local Quantum Physics
book, January 1996

Bulk emergence and the RG flow of entanglement entropy
journal, May 2015

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz
journal, April 1996

Recursive representation of the torus 1-point conformal block
journal, January 2010

Thermal fluctuations in quantized chaotic systems
journal, February 1996

Holographic entanglement entropy from 2d CFT: heavy states and local quenches
journal, February 2015

Recursive representation of the torus 1-point conformal block
text, January 2009

Bulk Emergence and the RG Flow of Entanglement Entropy
text, January 2014

Virasoro Conformal Blocks and Thermality from Classical Background Fields
text, January 2015

Eikonalization of Conformal Blocks
text, January 2015

Eigenstate Thermalization Hypothesis in Conformal Field Theory
text, January 2016

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
text, January 2017

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
text, January 1994

Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
journal, December 1997

Thermal correlation functions of KdV charges in 2D CFT
journal, February 2019

Generalized Gibbs ensemble and the statistics of KdV charges in 2D CFT
journal, March 2019

Entanglement entropy in (1+1)D CFTs with multiple local excitations
journal, May 2018

Generalized Gibbs Ensemble and the Statistics of KdV Charges in 2D CFT
text, January 2018

Exact generalized partition function of 2D CFTs at large central charge
journal, May 2019

Rényi entropy at large energy density in 2D CFT
journal, August 2019

The bulk-to-boundary propagator in black hole microstate backgrounds
journal, June 2019

Eigenstate thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach
journal, October 2019

Thermal Correlation Functions of KdV Charges in 2D CFT
text, January 2018

Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
journal, January 2019

Note on ETH of descendant states in 2D CFT
journal, January 2019

Probing thermality beyond the diagonal
text, January 2018

Entanglement entropy in (1+1)D CFTs with multiple local excitations
text, January 2018

The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
preprint, January 2018

Thermal Correlation Functions of KdV Charges in 2D CFT
text, January 2018

Exact generalized partition function of 2D CFTs at large central charge
text, January 2018

Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
journal, January 2019

Zero modes of local operators in 2d CFT on a cylinder
journal, July 2020