Stripping the planar Quantum Compass Model to its basics

TL;DR

This paper develops a new mean-field theory respecting the symmetries of the planar quantum compass model, revealing a first-order transition between dual nematic phases and uncovering novel orbital-spin separation phenomena.

Contribution

A novel mean-field approach that respects lower-dimensional symmetries of the quantum compass model and reveals new phase transition and orbital-spin separation insights.

Findings

First-order transition between dual nematic phases

Identification of fermion bound states as pseudo-spin-flip excitations

Implications for orbital and magnetic phase emergence

Abstract

We introduce a novel mean-field theory (MFT) around the exactly soluble two-leg ladder limit for the planar quantum compass model (QCM). In contrast to usual MFT, our construction respects the stringent constraints imposed by emergent, lower (here $d=1$) dimensional symmetries of the QCM. Specializing our construction to the QCM on a periodic four-leg ladder, we find that a first-order transition separates two mutually dual Ising nematic phases, in good accord with state-of-the-art numerics for the planar QCM. One pseudo-spin-flip excitation in the ordered phase turns out to be two (Jordan-Wigner) fermion bound states, reminiscent of spin waves in spin-$1/2$ Heisenberg chains. We discuss the novel implications of our work on (1) the emergence of coupled orbital and magnetic ordered and liquidlike disordered phases, and (2) a rare instance of orbital-spin separation in $d>1$, in the context of a Kugel-Khomskii view of multi-orbital Mott insulators.