Low-energy excitations in two-leg and three-leg quantum spin ladders Original Research Article

Low-energy excitations in spin-12 antiferromagnetic (AF) Heisenberg spin ladders are studied by bosonization and in a gauge-theoretical description. The AF Heisenberg models on ladders are described by spin-12 fermions and the systems are reduced to relativistic gauge theories of fermions by a mean-field type decoupling and linearization of the fermionʹs dispersion relation near Fermi points. There the gauge field is nothing other that phase degrees of freedom of the “mean field” on links. It is explicitly shown that zero-modes of boson fields for the bosonization of fermions play an essential role in obtaining correct results. In the two-leg case, the lowest-energy excitations are a spin-triplet magnon and they are described by three massive Majorana fermions. 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 bottom chains is introduced, a phase transition occurs at some critical coupling. Above the critical coupling, the system acquires an energy gap and low-energy excitations are a spin-triplet magnon and a spin-singlet excitation.