Gauge theory description of spin chains and ladders

An S = 1/2 antiferromagnetic spin chain is mapped to the two-flavor massles s Schwinger model, which admits a gapless mode. In a spin ladder system, ru ng interactions break the chiral invariance. These systems are solved by bo sonization. If the number of legs in a cyclically symmetric ladder system i s even, all of the gapless modes of spin chains become gapful. However, if the number of legs is odd, one combination of the gapless modes remains gap less. For a two-leg system we find that the spin gap is about .36 \J'\ when the interchain Heisenberg coupling J' is small compared with the intrachai n Heisenberg coupling.