skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Holographic entropy inequalities and gapped phases of matter

Abstract

Here, we extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holo-graphic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

Authors:
 [1];  [2];  [3];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Inst. for Quantum Information and Matter and Walter Burke Inst. for Theoretical Physics
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  3. Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1455189
Grant/Contract Number:  
SC0011632
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: 2015; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Holography and condensed matter physics (AdS/CMT); Topological States of Matter

Citation Formats

Bao, Ning, Cao, ChunJun, Walter, Michael, and Wang, Zitao. Holographic entropy inequalities and gapped phases of matter. United States: N. p., 2015. Web. doi:10.1007/JHEP09(2015)203.
Bao, Ning, Cao, ChunJun, Walter, Michael, & Wang, Zitao. Holographic entropy inequalities and gapped phases of matter. United States. doi:https://doi.org/10.1007/JHEP09(2015)203
Bao, Ning, Cao, ChunJun, Walter, Michael, and Wang, Zitao. Tue . "Holographic entropy inequalities and gapped phases of matter". United States. doi:https://doi.org/10.1007/JHEP09(2015)203. https://www.osti.gov/servlets/purl/1455189.
@article{osti_1455189,
title = {Holographic entropy inequalities and gapped phases of matter},
author = {Bao, Ning and Cao, ChunJun and Walter, Michael and Wang, Zitao},
abstractNote = {Here, we extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holo-graphic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.},
doi = {10.1007/JHEP09(2015)203},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2015,
place = {United States},
year = {2015},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006


Entanglement entropy of gapped phases and topological order in three dimensions
journal, November 2011


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


A New Inequality for the von Neumann Entropy
journal, May 2005


Holographic Duality with a View Toward Many-Body Physics
journal, January 2010


Six New Non-Shannon Information Inequalities
conference, July 2006

  • Dougherty, Randall; Freiling, Christopher; Zeger, Kenneth
  • 2006 IEEE International Symposium on Information Theory
  • DOI: 10.1109/ISIT.2006.261840

Topological Entanglement Entropy
journal, March 2006


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


Area Laws in Quantum Systems: Mutual Information and Correlations
journal, February 2008


Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture
journal, March 2006


Lectures on holographic methods for condensed matter physics
journal, October 2009


On characterization of entropy function via information inequalities
journal, July 1998

  • Zhen Zhang, ; Yeung, R. W.
  • IEEE Transactions on Information Theory, Vol. 44, Issue 4
  • DOI: 10.1109/18.681320

Aspects of holographic entanglement entropy
journal, August 2006


A non-Shannon-type conditional inequality of information quantities
journal, January 1997

  • Zhang, Z.; Yeung, R. W.
  • IEEE Transactions on Information Theory, Vol. 43, Issue 6
  • DOI: 10.1109/18.641561

Stabilizer information inequalities from phase space distributions
journal, August 2013

  • Gross, David; Walter, Michael
  • Journal of Mathematical Physics, Vol. 54, Issue 8
  • DOI: 10.1063/1.4818950

The holographic entropy cone
journal, September 2015

  • Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)130

An area law for one-dimensional quantum systems
journal, August 2007


Quantum Computation
conference, January 2012

  • Preskill, John
  • Proceedings of the 17th International Conference, General Relativity and Gravitation
  • DOI: 10.1142/9789812701688_0014

    Works referencing / citing this record:

    Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space
    journal, April 2018


    Analysing causal structures with entropy
    journal, November 2017

    • Weilenmann, Mirjam; Colbeck, Roger
    • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2207
    • DOI: 10.1098/rspa.2017.0483

    Space from Hilbert space: Recovering geometry from bulk entanglement
    journal, January 2017


    Majorana dimers and holographic quantum error-correcting codes
    journal, November 2019