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Entanglement spectrum and boundary theories with projected entangled-pair states

Cirac, J. Ignacio and Poilblanc, Didier and Schuch, Norbert and Vestraete, Frank (2011) Entanglement spectrum and boundary theories with projected entangled-pair states. Physical Review B, 83 (24). Art. No. 245134. ISSN 1098-0121.

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In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated with their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using projected entangled-pair states. This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models: a deformed AKLT model [I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)], an Ising-type model [F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)], and Kitaev’s toric code [A. Kitaev, Ann. Phys. 303, 2 (2003)], both in finite ladders and in infinite square lattices. In the second case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield nonlocal Hamiltonians. Because our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.

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Additional Information:© 2011 American Physical Society. Received 21 March 2011; revised 21 April 2011; published 29 June 2011. We acknowledge the hospitality of the Kavli Institute for Theoretical Physics (University of California, Santa Barbara) where this work was initiated. DP acknowledges support by the French Research Council (Agence Nationale de la Recherche) under Grant No. ANR 2010 BLANC 0406-01 and thanks IDRIS (Orsay, France) and CALMIP (Toulouse, France) for the use of NEC-SX8 and Altix SGI supercomputers, respectively. NS acknowledges support by the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information, NSF Grant No. PHY-0803371, and ARO Grant No. W911NF-09-1-0442. FV acknowledges funding from the SFB projects Vicom and Foqus and the EC projects QUERG and Quevadis. JIC acknowledges the EC project Quevadis, the DFG Forschergruppe 635, and Caixa Manresa.
Funding AgencyGrant Number
French Research Council (Agence Nationale de la Recherche)ANR 2010 BLANC 0406-01
Gordon and Betty Moore FoundationUNSPECIFIED
Army Research Office (ARO)W911NF-09-1-0442
SFB projects Vicom and FoqusUNSPECIFIED
EC projects QUERG and QuevadisUNSPECIFIED
DFG Forschergruppe 635UNSPECIFIED
Issue or Number:24
Classification Code:PACS: 71.10.-w, 03.67.-a, 02.70.-c
Record Number:CaltechAUTHORS:20110718-114035840
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24449
Deposited By: Jason Perez
Deposited On:18 Jul 2011 20:45
Last Modified:03 Oct 2019 02:56

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