Resonating valence bonds states in the PEPS formalism

Details Resonating valence bonds states in the PEPS formalism Resonating valence bonds states in the PEPS formalism

2012-03-21

arxiv.org/abs/1203.4816v1

Physics

Condensed Matter

Strongly Correlated Electrons

9+9 pages, 28 figures

Scientific paper

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 four-fold degenerate ground state of a local Hamiltonian on the (finite) kagome lattice. Using numerical methods, we study whether this interpolation exhibits a phase transition: We find that all studied correlation functions behave smoothly, whereas the overlap of the wavefunction shows possible signs of a high-order phase transition.

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