  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.
