Quantum dimer model

The quantum dimer model was introduced by Rokhsar and Kivelson Physical Review Letters 61, 2376 (1988) as an effective theory for the low-lying singlet excitations above paramagnetic ground states of quantum antiferromagnets. It was shown in paper 1 and paper 3 that a dual theory of such models on bipartite lattices was essentially identical to models obtained from a semiclassical theory of the quantum fluctuations of the Neel order. The results described in this web page then immediately implied that the quantum dimer model generically had only "crystalline" phases (in which the dimers spontaneously break translational symmetry) on such lattices (isolated critical points without crystalline order are allowed).

The properties of quantum dimer models on non-bipartite lattices (more precisely, for antiferromagnets in which the classical ground state had non-collinear order) were discussed in papers 4,5,6,7. The connection with a Z2 gauge theory (and the closely related theory of a compact U(1) gauge field coupled to charge 2 Higgs scalars) was made, and the results on this web page then implied that such models could have "spin-liquid" or RVB states. In particular, paper 6 was the first to suggest that such states should exist for the quantum dimer model on the kagome and triangular lattices.

The above predictions have been verified in studies by Moessner and Sondhi, Physical Review Letters 86, 1881 (2001), Moessner, Sondhi, and Chandra, Physical Review B 64, 144416 (2001), Moessner, Sondhi, and Fradkin, Physical Review B 65, 024504 (2002), Ioffe, Feigel'man, Ioselevich, Ivanov, Troyer, and Blatter Nature 415, 503 (2002) and Misguich, Serban, and Pasquier cond-mat/0204428.


  1. Sine-Gordon theory of the non-Neel phase of two-dimensional quantum antiferromagnets, W. Zheng and S. Sachdev, Physical Review B 40, 2704 (1989).
  2. Spin-Peierls ground states of the quantum dimer model: a finite size study, S. Sachdev, Physical Review B 40, 5204 (1989).
  3. Spin-Peierls, valence bond solid, and Neel ground states of low dimensional quantum antiferromagnets, N. Read and S. Sachdev, Physical Review B 42, 4568 (1990) --- see Appendix A.
  4. Duality mappings for quantum dimers, S. Sachdev, unpublished notes dated July 30, 1990. The final results of these notes were announced in paper 5, and full details were published in paper 7.
  5. Spontaneous alignment of frustrated bonds in an anisotropic, three dimensional Ising model, R. Jalabert and S. Sachdev, Physical Review B 44, 686 (1991).
  6. Kagome and triangular lattice Heisenberg antiferromagnets: ordering from quantum fluctuations and quantum-disordered ground states with deconfined bosonic spinons, S. Sachdev, Physical Review B 45, 12377 (1992).
  7. Translational symmetry breaking in two-dimensional antiferromagnets and superconductors, S. Sachdev and M. Vojta, Journal of the Physical Society of Japan 69, Suppl. B, 1 (2000); cond-mat/9910231.
  8. Field theories of paramagnetic Mott insulators, S. Sachdev, Proceedings of the International Conference on Theoretical Physics, Paris, UNESCO, 22-27 July 2002, Annales Henri Poincare 4, 559 (2003); cond-mat/0304137.