SO(5)-symmetric description of the low-energy sector of a ladder system

We study a system of two Tomonaga-Luttinger models coupled by a small transverse hopping (a two-chain ladder). We use Abelian and non-Abelian bosonization to show that the strong coupling regime at low energies can be described by an $\mathrm{SO}(5{)}_1$ Wess-Zumino-Witten model (or equivalently five massless Majorana fermions) deformed by symmetry-breaking terms that nonetheless leave the theory critical at $T=0.\mathrm{}$ The SO(5) currents of the theory comprise the charge and spin currents and linear combinations of the so-called pi operators [S.C. Zhang, Science $275,$ 1089 (1997)], which are local in terms both of the original fermions and those of the effective theory. Using bosonization we obtain the asymptotic behavior of all correlation functions. We find that the five-component “superspin” vector has power-law correlations at $T=0;$ other fermion bilinears have exponentially decaying correlations and the corresponding tendencies are suppressed. Conformal field theory also allows us to obtain the energies, quantum numbers, and degeneracies of the low-lying states and fit them into deformed SO(5) multiplets.