Approximate SO(5) Symmetry in the Low Energy Sector of a Ladder System

Preprint
Publisher Website
Google Scholar
  • 24 October 1997
Abstract
We present the first example of a realistic physical model where it can explicitly be shown that an approximate SO(5) symmetry emerges at intermediate energy scales. Specifically, we study a system of two Tomonaga-Luttinger models in the repulsive regime coupled by a small transverse hopping (a two-chain ladder). We use careful Abelian and non-Abelian bosonisation to show that the strong coupling regime at low energies can be described by an SO(5)$_1$ WZW model or equivalently 5 massless Majorana fermions, perturbed by symmetry breaking terms which nonetheless leave the theory critical at T=0. 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 bosonisation we can obtain the asymptotic behaviour of all correlation functions. We find that the 5 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 SO(5) multiplets.

This publication has 0 references indexed in Scilit: