Holographic entropy inequalities and gapped phases of matter

Bao, Ning; Cao, ChunJun; Walter, Michael; Wang, Zitao

doi:10.1007/JHEP09(2015)203

Title: Holographic entropy inequalities and gapped phases of matter

Journal Article · Tue Sep 29 00:00:00 EDT 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP09(2015)203· OSTI ID:1455189

Bao, Ning ^[1]; Cao, ChunJun ^[2]; Walter, Michael ^[3]; Wang, Zitao ^[1]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Inst. for Quantum Information and Matter and Walter Burke Inst. for Theoretical Physics
California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics

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.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

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

Grant/Contract Number:: SC0011632

OSTI ID:: 1455189

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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References (17)

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.181602	journal	May 2006
Entanglement entropy of gapped phases and topological order in three dimensions Grover, Tarun; Turner, Ari M.; Vishwanath, Ashvin Physical Review B, Vol. 84, Issue 19 https://doi.org/10.1103/PhysRevB.84.195120	journal	November 2011
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
A New Inequality for the von Neumann Entropy Linden, Noah; Winter, Andreas Communications in Mathematical Physics, Vol. 259, Issue 1 https://doi.org/10.1007/s00220-005-1361-2	journal	May 2005
Holographic Duality with a View Toward Many-Body Physics McGreevy, John Advances in High Energy Physics, Vol. 2010 https://doi.org/10.1155/2010/723105	journal	January 2010
Six New Non-Shannon Information Inequalities Dougherty, Randall; Freiling, Christopher; Zeger, Kenneth 2006 IEEE International Symposium on Information Theory https://doi.org/10.1109/ISIT.2006.261840	conference	July 2006
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
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
Area Laws in Quantum Systems: Mutual Information and Correlations Wolf, Michael M.; Verstraete, Frank; Hastings, Matthew B. Physical Review Letters, Vol. 100, Issue 7 https://doi.org/10.1103/PhysRevLett.100.070502	journal	February 2008
Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture Gioev, Dimitri; Klich, Israel Physical Review Letters, Vol. 96, Issue 10 https://doi.org/10.1103/PhysRevLett.96.100503	journal	March 2006
Lectures on holographic methods for condensed matter physics Hartnoll, Sean A. Classical and Quantum Gravity, Vol. 26, Issue 22 https://doi.org/10.1088/0264-9381/26/22/224002	journal	October 2009
On characterization of entropy function via information inequalities IEEE Transactions on Information Theory, Vol. 44, Issue 4 https://doi.org/10.1109/18.681320	journal	July 1998
Aspects of holographic entanglement entropy Ryu, Shinsei; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2006, Issue 08 https://doi.org/10.1088/1126-6708/2006/08/045	journal	August 2006
A non-Shannon-type conditional inequality of information quantities Zhang, Z.; Yeung, R. W. IEEE Transactions on Information Theory, Vol. 43, Issue 6 https://doi.org/10.1109/18.641561	journal	January 1997
Stabilizer information inequalities from phase space distributions Gross, David; Walter, Michael Journal of Mathematical Physics, Vol. 54, Issue 8 https://doi.org/10.1063/1.4818950	journal	August 2013
The holographic entropy cone Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)130	journal	September 2015
Quantum Computation Preskill, John Proceedings of the 17th International Conference, General Relativity and Gravitation https://doi.org/10.1142/9789812701688_0014	conference	January 2012

Cited By (7)

Analysing causal structures with entropy Weilenmann, Mirjam; Colbeck, Roger Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2207 https://doi.org/10.1098/rspa.2017.0483	journal	November 2017
Majorana dimers and holographic quantum error-correcting codes Jahn, A.; Gluza, M.; Pastawski, F. Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/physrevresearch.1.033079	journal	November 2019
Majorana dimers and holographic quantum error-correcting codes Jahn, A.; Gluza, M.; Pastawski, F. Freie Universität Berlin https://doi.org/10.17169/refubium-26816	text	January 2019
Space from Hilbert Space: Recovering Geometry from Bulk Entanglement Cao, ChunJun; Carroll, Sean M.; Michalakis, Spyridon arXiv https://doi.org/10.48550/arxiv.1606.08444	text	January 2016
Analysing causal structures with entropy Weilenmann, Mirjam; Colbeck, Roger arXiv https://doi.org/10.48550/arxiv.1709.08988	text	January 2017
Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space Cao, ChunJun; Carroll, Sean M. arXiv https://doi.org/10.48550/arxiv.1712.02803	text	January 2017
Holographic Renyi Entropy from Quantum Error Correction Akers, Chris; Rath, Pratik arXiv https://doi.org/10.48550/arxiv.1811.05171	text	January 2018

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