Quantum dimer models and effective Hamiltonians on the pyrochlore lattice

R. Moessner, Shivaji Lal Sondhi, M. O. Goerbig

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24 Scopus citations


We study a large- N deformation of the S=1 2 pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading nontrivial order. In this limit, the ground state manifold-while extensively degenerate-breaks the inversion symmetry of the lattice, which implies a finite temperature Ising transition without translational symmetry breaking. At lower temperatures and further in the 1 N expansion, we discuss an effective Hamiltonian within the degenerate manifold, which has a transparent physical interpretation as representing dimer potential energies. We find mean-field ground states of the effective Hamiltonian which exhibit translational symmetry breaking. The entire scenario offers a new perspective on previous treatments of the SU(2) problem not controlled by a small parameter, in particular showing that a mean-field state considered previously encodes the physics of a maximally flippable dimer configuration. We also comment on the difficulties of extending our results to the SU(2) case, and note implications for classical dimer models.

Original languageEnglish (US)
Article number094430
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number9
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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