Spin gap in low-dimensional Mott insulators with orbital degeneracy

TL;DR

This study investigates the ground state properties of a model describing orbital degeneracy in low-dimensional Mott insulators, revealing a valence bond crystal in 1D and a potential spin liquid in 2D, using Green's Function Monte Carlo methods.

Contribution

It provides the first detailed numerical analysis of a coupled spin-orbital model, suggesting a spin liquid state in two dimensions.

Findings

1D ground state is a valence bond crystal.

2D spin gap remains finite, no long-range magnetic order.

No evidence of valence bond crystal in 2D, indicating a possible spin liquid.

Abstract

We consider the exchange Hamiltonian H_ST = -J Sum_{<rr'>} (2 S_r S_r' - 1/2) (2 T_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 valence bond crystal. A spin liquid appears as a plausible scenario compatible with our findings.