Columnar phase in quantum dimer models

Alessandro Giuliani, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The quantum dimer model, relevant for short-range resonant valence bond physics, is rigorously shown to have long range order in a crystalline phase in the attractive case at low temperature and not too large flipping term. This term flips horizontal dimer pairs to vertical pairs (and vice versa) and is responsible for the word 'quantum' in the title. In addition to the dimers, monomers are also allowed. The mathematical method used is 'reflection positivity'. The model and proof can easily be generalized to dimers or plaquettes in three-dimensions.

Original languageEnglish (US)
Article number235203
JournalJournal of Physics A: Mathematical and Theoretical
Issue number23
StatePublished - Jun 10 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


  • crystalline long range order
  • quantum dimmers
  • reflection positivity


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