Doping quantum dimer models on the square lattice
Résumé
A family of models is proposed to describe the motion of holes injected in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (NY) {\bf 318}, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at finite doping which can be mapped on a doped interacting classical dimer model is constructed. More general models are also considered with arbitrary values of dimer-flip and hole hopping amplitudes, as well as dimer-dimer repulsion. Hole-hole correlations are investigated by Exact Diagonalization, Green's function and classical Monte Carlo methods. Upon increasing dimer repulsion, deconfinement abruptly appears in the staggered phase. In the generalized Rokhsar-Kivelson doped quantum dimer model derived here deconfinement occurs in the critical spin-liquid phase. We also conjecture the existence of two-hole bound states in some region of this deconfined phase.