Nonperturbative effective-field theory for two-leg antiferromagnetic spin ladders

Abstract

We study the long wavelength limit of a spin-½ Heisenberg antiferromagnetic two-leg ladder, treating the interchain coupling in a nonperturbative way. We perform a mean field analysis and then include the fluctuations in an exact way. This allows for a discussion of the phase diagram of the system and provides an effective-field theory for the low-energy excitations. The coset fermionic Lagrangian obtained corresponds toa perturbed SU(4)₁ / U(1) conformal field theory (CFT). This effective theory is naturally embedded in a SU(2)₂ x Z₂ CFT, where perturbations are easily identified in terms of conformal operators in the two sectors. Crossed and zigzag ladders are also discussed using the same approach.