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:

• P. W. Kasteleyn, Physica 27, 1209 (1961)
• M. E. Fisher, Phys. Rev. 124, 1664 (1961).

Introduction of model; early literature:

• S.A. Kivelson, D.S. Rokhsar, and J.P. Sethna, Phys. Rev. B 35, 8865 (1987).
• D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).

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

• R. Moessner and S.L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001).
• G. Misguich, D. Serban, and V. Pasquier, Phys. Rev. Lett. 89, 137202 (2002).

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

• N. Read and Subir Sachdev, Large-N expansion for frustrated quantum antiferromagnets, Phys. Rev. Lett. 66 1773 (1991)
• Xiao-Gang Wen, Mean Field Theory of Spin Liquid States with Finite Energy Gaps, Phys. Rev. B 44 2664 (1991)