FM 01-15; arXiv:1502.02254

Authors: Alessandro Giuliani, Elliott H. Lieb

Title: Columnar Phase in Quantum Dimer Models

Sommario: 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 3-dimensions.

Alessandro Giuliani
Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, 00146 Roma Italy
giuliani@mat.uniroma3.it

Elliott H. Lieb
Departments of Mathematics and Physics, Jadwin Hall, Princeton University Princeton 08544 NJ, USA
lieb@math.princeton.edu