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Quantum dimer models

{{short description|Model of the physics of resonating valence bond states in lattice spin systems}}

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:

  • {{cite journal | last=Kasteleyn | first=P.W. | title=The statistics of dimers on a lattice | journal=Physica | publisher=Elsevier BV | volume=27 | issue=12 | year=1961 | issn=0031-8914 | doi=10.1016/0031-8914(61)90063-5 | pages=1209–1225 | bibcode=1961Phy....27.1209K}}
  • {{cite journal | last=Fisher | first=Michael E. | title=Statistical Mechanics of Dimers on a Plane Lattice | journal=Physical Review | publisher=American Physical Society (APS) | volume=124 | issue=6 | date=15 December 1961 | issn=0031-899X | doi=10.1103/physrev.124.1664 | pages=1664–1672| bibcode=1961PhRv..124.1664F }}

Introduction of model; early literature:

  • {{cite journal | last1=Kivelson | first1=Steven A. | last2=Rokhsar | first2=Daniel S. | last3=Sethna | first3=James P. | title=Topology of the resonating valence-bond state: Solitons and high-Tc superconductivity | journal=Physical Review B | publisher=American Physical Society (APS) | volume=35 | issue=16 | date=1 May 1987 | issn=0163-1829 | doi=10.1103/physrevb.35.8865 | pages=8865–8868 | pmid=9941277 | bibcode=1987PhRvB..35.8865K}}
  • {{cite journal | last1=Rokhsar | first1=Daniel S. | last2=Kivelson | first2=Steven A. | title=Superconductivity and the Quantum Hard-Core Dimer Gas | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=61 | issue=20 | date=14 November 1988 | issn=0031-9007 | doi=10.1103/physrevlett.61.2376 | pages=2376–2379| pmid=10039096 | bibcode=1988PhRvL..61.2376R }}

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

  • {{cite journal|last1=Jalabert|first1=Rodolfo A.|last2=Sachdev|first2=Subir|title=Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model|journal=Physical Review B|volume=44|issue=2|year=1991|pages=686–690|issn=0163-1829|doi=10.1103/PhysRevB.44.686|pmid=9999168|bibcode=1991PhRvB..44..686J}}; {{cite journal

|last1=Sachdev

|first1=S.

|last2=Vojta

|first2=M.

|url=https://journals.jps.jp/page/jpsj/suppl

|date=1999

|title=Translational symmetry breaking in two-dimensional antiferromagnets and superconductors

|journal=J. Phys. Soc. Jpn.

|volume = 69, Supp. B

|pages = 1

|arxiv = cond-mat/9910231|bibcode=1999cond.mat.10231S

}}

  • {{cite journal | last1=Moessner | first1=R. | last2=Sondhi | first2=S. L. | title=Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model | journal=Physical Review Letters | volume=86 | issue=9 | date=26 February 2001 | issn=0031-9007 | doi=10.1103/physrevlett.86.1881 | pages=1881–1884| pmid=11290272 | arxiv=cond-mat/0007378 | bibcode=2001PhRvL..86.1881M | s2cid=19284848 }}
  • {{cite journal | last1=Misguich | first1=G. | last2=Serban | first2=D. | last3=Pasquier | first3=V. | title=Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory | journal=Physical Review Letters | volume=89 | issue=13 | date=6 September 2002 | issn=0031-9007 | doi=10.1103/physrevlett.89.137202 | page=137202| pmid=12225059 | arxiv=cond-mat/0204428 | bibcode=2002PhRvL..89m7202M | s2cid=30393136 }}

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

  • {{cite journal | last1=Read | first1=N. | last2=Sachdev | first2=Subir | title=Large-Nexpansion for frustrated quantum antiferromagnets | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=66 | issue=13 | date=1 March 1991 | issn=0031-9007 | doi=10.1103/physrevlett.66.1773 | pages=1773–1776 | pmid=10043303 | bibcode=1991PhRvL..66.1773R}}
  • {{cite journal | last=Wen | first=X. G. | title=Mean-field theory of spin-liquid states with finite energy gap and topological orders | journal=Physical Review B | publisher=American Physical Society (APS) | volume=44 | issue=6 | date=1 July 1991 | issn=0163-1829 | doi=10.1103/physrevb.44.2664 | pages=2664–2672 | bibcode=1991PhRvB..44.2664W | pmid=9999836}}

Category:Quantum lattice models

Category:Condensed matter physics

Category:Statistical mechanics

Category:Matching (graph theory)

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