Stripping the planar quantum compass model to its basics

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