Valence Bond Crystal and possible orbital pinball liquid in a t2g model

TL;DR

This paper investigates a model for orbitally degenerate Mott insulators, revealing two distinct fluctuating regimes with different ground states: a valence bond crystal with orbital singlets and a resonating orbital state with long-range order.

Contribution

It introduces a detailed analysis of the competing exchange mechanisms in t2g models, identifying and characterizing two novel fluctuating phases with distinct orbital arrangements.

Findings

Superexchange regime exhibits a valence bond crystal with orbital singlets.

Direct exchange regime shows a resonating ground state with long-range orbital order.

Effective models and numerical analysis support the phase distinctions.

Abstract

We study a model for orbitally degenerate Mott insulators, where localized electrons possess t_2g degrees of freedom coupled by several, competing, exchange mechanisms. We provide evidence for two distinct strongly fluctuating regimes, depending on whether superexchange or direct exchange mechanism predominates. In the superexchange-dominated regime, the ground state is dimerized, with nearest neighbor orbital singlets covering the lattice. By deriving an effective quantum dimer model and analyzing it numerically, we characterize this dimerized phase as a valence bond crystal stabilized by singlet resonances within a large unit cell. In the opposite regime, with predominant direct exchange, the combined analysis of the original model and another effective model adapted to the local constraints, shows that subleading perturbations select a highly resonating ground state, with coexisting diagonal and off-diagonal long-range orbital orders.