Spin gap in low-dimensional Mott insulators with orbital degeneracy

Abstract

We consider the exchanged Hamiltonian HST=−J∑〈rr′〉(2Sr⋅Sr′−12)(2Tr⋅Tr′−12), describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on equivalent bonds. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit. To investigate the ground state properties we use a Green’s Function Monte Carlo, calculating energy gaps and correlation functions, the latter through the forward walking technique. In one dimension we find that the ground state is a “crystal” of valence bond dimers. In two dimensions, the spin gap appears to remain finite in the thermodynamic limit, and, consistently, the staggered magnetization—signal of Néel long range order—seems to vanish. From the analysis of dimer–dimer correlation functions, however, we find no sign of a valance bond crystal. A spin liquid appears as a plausible scenario compatible with our findings.