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Resonating valence bond states in the PEPS formalism

Schuch, Norbert and Poilblanc, Didier and Cirac, J. Ignacio and Pérez-García, David (2012) Resonating valence bond states in the PEPS formalism. Physical Review B, 86 (11). Art. No. 115108. ISSN 1098-0121.

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We study resonating valence bond (RVB) states in the projected entangled pair states (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the SU(2) singlet RVB state on the kagome lattice: We prove the equivalence of toric code and dimer state, and devise an interpolation between the dimer state and the RVB state. This interpolation corresponds to a continuous path in Hamiltonian space, proving that the RVB state is the fourfold degenerate ground state of a local Hamiltonian on the (finite) kagome lattice. We investigate this interpolation using numerical PEPS methods, studying the decay of correlation functions, the change of overlap, and the entanglement spectrum, none of which exhibits signs of a phase transition.

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Additional Information:© 2012 American Physical Society. Received 30 April 2012; published 7 September 2012. We acknowledge helpful comments by S. Kivelson and A. Seidel. We wish to thank the Perimeter Institute for Theoretical Physics in Waterloo, Canada, and the Centro de Ciencias Pedro Pascual in Benasque, Spain, where parts of this work were carried out, for their hospitality. N.S. acknowledges support by the Alexander von Humboldt Foundation, the Caltech Institute for Quantum Information and Matter (an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation), and NSF Grant No. PHY-0803371. D.P. acknowledges support by the “Agence Nationale de la Recherche” under Grant No. ANR 2010 BLANC 0406-0, and CALMIP (Toulouse) for supercomputer resources under Project No. P1231. J.I.C. acknowledges the EU project QUEVADIS, the DFG Forschergruppe 635, and Caixa Manresa. D.P.-G. acknowledges QUEVADIS and Spanish grants QUITEMAD and MTM2011-26912.
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Alexander von Humboldt FoundationUNSPECIFIED
Caltech Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Agence Nationale de la Recherche (ANR)ANR 2010 BLANC 0406-0
CALMIP (Toulouse)P1231
DFG Forschergruppe635
Spanish GrantMTM2011-26912
Classification Code:PACS: 03.65.Vf, 75.10.Kt
Record Number:CaltechAUTHORS:20121005-094538673
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34702
Deposited By: Tony Diaz
Deposited On:05 Oct 2012 20:20
Last Modified:27 Dec 2012 02:49

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