Spin gap in low-dimensional Mott insulators with orbital degeneracy

We consider the exchanged Hamiltonian H-ST = -J Sigma((rr')) (2S(r). S-r' -1/2)( 2T(r'). T-r' -1/2), 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 Neel 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. (C) 1999 American Institute of Physics. [S0021-8979(99)53908-X].