LOW-ENERGY EXCITATIONS IN 2-LEG AND 3-LEG QUANTUM SPIN LADDERS

Low-energy excitations in spin-1/2 antiferromagnetic (AF) Heisenberg s pin ladders are studied by bosonization and in a gauge-theoretical des cription. The AF Heisenberg models on ladders are described by spin-1/ 2 fermions and the systems are reduced to relativistic gauge theories of fermions by a mean-field type decoupling and linearization of the f ermion's dispersion relation near Fermi points, There the gauge field is nothing other that phase degrees of freedom of the ''mean field'' o n links. It is explicitly shown that zero-modes of boson fields for th e bosonization of fermions play an essential role in obtaining correct results. In the two-leg case, the lowest-energy excitations are a spi n-triplet magnon and they are described by three massive Majorana ferm ions. On the other hand, in the three-leg system, spin excitations on the top and bottom chains are described by two massless boson fields. It is predicted that if interaction between spins on the top and botto m chains is introduced, a phase transition occurs at some critical cou pling. Above the critical coupling, the system acquires an energy gap and low-energy excitations are a spin-triplet magnon and a spin-single t excitation, (C) 1998 Elsevier Science B.V.