Bipartite Rokhsar-Kivelson points and Cantor deconfinement

Eduardo Fradkin, David A. Huse, R. Moessner, V. Oganesyan, Shivaji Lal Sondhi

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165 Scopus citations


Quantum dimer models on bipartite lattices exhibit Rokhsar-Kivelson points with exactly known critical ground states and deconfined spinons. We examine generic, weak perturbations around these points. In d=2 + 1 we find a first-order transition between a "plaquette" valence bond crystal and a region with a devil's staircase of commensurate and incommensurate valence bond crystals. In the part of the phase diagram where the staircase is incomplete, the incommensurate states exhibit a gapless photon and deconfined spinons on a set of finite measure, almost but not quite a deconfined phase in a compact U(1) gauge theory in d=2+1! In d=3+1, we find a continuous transition between the U(1) resonating valence bond phase and a deconfined staggered valence bond crystal. In an appendix, we comment on analogous phenomena in quantum vertex models, most notably the existence of a continuous transition on the triangular lattice in d=2+1.

Original languageEnglish (US)
Article number224415
Pages (from-to)224415-1-224415-8
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number22
StatePublished - Jun 2004

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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