Exotic Mott phases of the extended t--J model on the checkerboard lattice at commensurate densities

TL;DR

This paper investigates exotic insulating phases in an extended t--J model on a checkerboard lattice at specific electron densities, revealing complex Mott states with plaquette order influenced by Coulomb interactions and spin degrees of freedom.

Contribution

It extends previous work on quarter-filled systems to 1/8 and 3/8 fillings, analyzing the nature of insulating phases and the role of spin in stabilizing plaquette order.

Findings

Identification of plaquette order at 1/4 and 3/4 fillings

Dependence of metal-insulator transition on Coulomb repulsion and hopping sign

Evidence of Resonating-Singlet-Pair Crystal phases with lattice symmetry preservation

Abstract

Coulomb repulsion between electrons moving on a frustrated lattice can give rise, at simple commensurate electronic densities, to exotic insulating phases of matter. Such a phenomenon is illustrated using an extended t--J model on a planar pyrochlore lattice for which the work on the quarter-filled case [cond-mat/0702367] is complemented and extended to 1/8- and 3/8-fillings. The location of the metal-insulator transition as a function of the Coulomb repulsion is shown to depend strongly on the sign of the hopping. Quite generally, the metal-insulator transition is characterized by lattice symmetry breaking but the nature of the insulating Mott state is more complex than a simple Charge Density Wave. Indeed, in the limit of large Coulomb repulsion, the physics can be described in the framework of (extended) quantum fully-packed loop or dimer models carrying extra spin degrees of freedom. Various diagonal and off-diagonal plaquette correlation functions are computed and the low-energy spectra are analyzed in details in order to characterize the nature of the insulating phases. We provide evidence that, as for an electronic density of n=1/2 (quarter-filling), the system at $n=1/4$ or $n=3/4$ exhibits also plaquette order by forming a (lattice rotationally-invariant) Resonating-Singlet-Pair Crystal, although with a quadrupling of the lattice unit cell (instead of a doubling for $n=1/2$) and a 4-fold degenerate ground state. Interestingly, qualitative differences with the bosonic analog (e.g. known to exhibit columnar order at n=1/4) emphasize the important role of the spin degrees of freedom in e.g. stabilizing plaquette phases w.r.t. rotational symmetry-breaking phases.