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Resonating valence bond states in the PEPS formalism

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Schuch, Norbert and Poilblanc, Didier and Cirac, Juan I. and Pérez García, David (2012) Resonating valence bond states in the PEPS formalism. Physical review B, 86 (11). ISSN 1098-0121

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Official URL: http://prb.aps.org/pdf/PRB/v86/i11/e115108


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Heisenberg-antiferromagnet; ground-states; quantum; phase
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:16764
Deposited On:18 Oct 2012 11:23
Last Modified:09 Dec 2014 08:59

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