Quantum dimer models

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Quantum dimer models were introduced to model the physics of resonating valence bond (RVB) states in . The only degrees of freedom retained from the motivating spin systems are the valence bonds, represented as dimers which live on the lattice bonds. In typical dimer models, the dimers do not overlap ("hardcore constraint").

Typical phases of quantum dimer models tend to be . However, on non-bipartite lattices, RVB liquid phases possessing topological order and fractionalized spinons also appear. The discovery of topological order in quantum dimer models (more than a decade after the models were introduced) has led to new interest in these models.

Classical dimer models have been studied previously in statistical physics, in particular by P. W. Kasteleyn (1961) and M. E. Fisher (1961).

References[]

Exact solution for classical dimer models on planar graphs:

  • Kasteleyn, P.W. (1961). "The statistics of dimers on a lattice". Physica. Elsevier BV. 27 (12): 1209–1225. Bibcode:1961Phy....27.1209K. doi:10.1016/0031-8914(61)90063-5. ISSN 0031-8914.
  • Fisher, Michael E. (15 December 1961). "Statistical Mechanics of Dimers on a Plane Lattice". Physical Review. American Physical Society (APS). 124 (6): 1664–1672. Bibcode:1961PhRv..124.1664F. doi:10.1103/physrev.124.1664. ISSN 0031-899X.

Introduction of model; early literature:

  • Kivelson, Steven A.; Rokhsar, Daniel S.; Sethna, James P. (1 May 1987). "Topology of the resonating valence-bond state: Solitons and high-Tc superconductivity". Physical Review B. American Physical Society (APS). 35 (16): 8865–8868. Bibcode:1987PhRvB..35.8865K. doi:10.1103/physrevb.35.8865. ISSN 0163-1829. PMID 9941277.
  • Rokhsar, Daniel S.; Kivelson, Steven A. (14 November 1988). "Superconductivity and the Quantum Hard-Core Dimer Gas". Physical Review Letters. American Physical Society (APS). 61 (20): 2376–2379. Bibcode:1988PhRvL..61.2376R. doi:10.1103/physrevlett.61.2376. ISSN 0031-9007. PMID 10039096.

Topological order in quantum dimer model on non-bipartite lattices:

Topological order in quantum spin model on non-bipartite lattices:


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