Quantum dimer models

Quantum dimer models were introduced to model the physics of resonating valence bond (RVB) states in lattice spin systems. 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 valence bond crystals. 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. 27 (12). Elsevier BV: 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. 124 (6). American Physical Society (APS): 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. 35 (16). American Physical Society (APS): 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. 61 (20). American Physical Society (APS): 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:

• Jalabert, Rodolfo A.; Sachdev, Subir (1991). "Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model". Physical Review B. 44 (2): 686–690. Bibcode:1991PhRvB..44..686J. doi:10.1103/PhysRevB.44.686. ISSN 0163-1829. PMID 9999168.; Sachdev, S.; Vojta, M. (1999). "Translational symmetry breaking in two-dimensional antiferromagnets and superconductors". J. Phys. Soc. Jpn. 69, Supp. B: 1. arXiv:cond-mat/9910231. Bibcode:1999cond.mat.10231S.

• Moessner, R.; Sondhi, S. L. (26 February 2001). "Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model". Physical Review Letters. 86 (9): 1881–1884. arXiv:cond-mat/0007378. Bibcode:2001PhRvL..86.1881M. doi:10.1103/physrevlett.86.1881. ISSN 0031-9007. PMID 11290272. S2CID 19284848.
• Misguich, G.; Serban, D.; Pasquier, V. (6 September 2002). "Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory". Physical Review Letters. 89 (13): 137202. arXiv:cond-mat/0204428. Bibcode:2002PhRvL..89m7202M. doi:10.1103/physrevlett.89.137202. ISSN 0031-9007. PMID 12225059. S2CID 30393136.

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

• Read, N.; Sachdev, Subir (1 March 1991). "Large-Nexpansion for frustrated quantum antiferromagnets". Physical Review Letters. 66 (13). American Physical Society (APS): 1773–1776. Bibcode:1991PhRvL..66.1773R. doi:10.1103/physrevlett.66.1773. ISSN 0031-9007. PMID 10043303.
• Wen, X. G. (1 July 1991). "Mean-field theory of spin-liquid states with finite energy gap and topological orders". Physical Review B. 44 (6). American Physical Society (APS): 2664–2672. Bibcode:1991PhRvB..44.2664W. doi:10.1103/physrevb.44.2664. ISSN 0163-1829. PMID 9999836.