Spin-orbital exchange of strongly interacting fermions on the $p$-band of a two-dimensional optical lattice

TL;DR

This paper investigates the spin-orbital exchange interactions in strongly interacting fermions on the $p$-band of a 2D optical lattice, revealing a spin-disordered ground state with ferro-orbital order and decoupled Heisenberg chains.

Contribution

It derives the spin-orbital exchange for fermions on the $p$-band and uncovers a novel spin-disordered phase with ferro-orbital order and chain-like behavior.

Findings

Ground state is spin-disordered with ferro-orbital order.

System behaves as decoupled Heisenberg spin chains.

Luttinger liquid behavior is accessible at higher temperatures.

Abstract

Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the $p$-band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the $p$-band when the density fluctuations are suppressed, and show it frustrates the development of long range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the $s$-band.