Shortranged resonating valence bond physics, quantum dimer models, and Ising gauge theories
Abstract
Quantum dimer models are believed to capture the essential physics of antiferromagnetic phases dominated by shortranged valence bond configurations. We show that these models arise as particular limits of Ising (Z_{2}) gauge theories, but that in these limits the system develops a larger local U(1) invariance that has different consequences on different lattices. Conversely, we note that the standard Z_{2} gauge theory is a generalized quantum dimer model, in which the particular relaxation of the hardcore constraint for the dimers breaks the U(1) down to Z_{2}. These mappings indicate that at least one realization of the SenthilFisher proposal for fractionalization is exactly the short ranged resonating valence bond (RVB) scenario of Anderson and of Kivelson, Rokhsar and Sethna. They also suggest that other realizations will require the identification of a local low energy, Ising link variable and a natural constraint. We also discuss the notion of topological order in Z_{2} gauge theories and its connection to earlier ideas in RVB theory. We note that this notion is not central to the experiment proposed by Senthil and Fisher to detect vortices in the conjectured Z_{2} gauge field.
 Publication:

Physical Review B
 Pub Date:
 January 2002
 DOI:
 10.1103/PhysRevB.65.024504
 arXiv:
 arXiv:condmat/0103396
 Bibcode:
 2002PhRvB..65b4504M
 Keywords:

 74.20.Mn;
 75.10.Jm;
 71.10.w;
 Nonconventional mechanisms;
 Quantized spin models;
 Theories and models of manyelectron systems;
 Condensed Matter  Superconductivity;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 17 pages, 4 postscript figures automatically included