Gauge theory description of spin ladders

An s = 1/2 antiferromagnetic spin chain is equivalent to the two-flavour massless Schwinger model in a uniform background charge density in the strong coupling regime. The gapless mode of the spin chain is represented by a massless boson of the Schwinger model. In a two-leg spin ladder system the massless boson aquires a finite mass due to inter-chain interactions. The gap energy is found to be about 0.36\J'\ when the inter-chain Heisenberg coupling J' is small compared with the intra-chain Heisenberg coupling. It is also shown that a cyclically symmetric N-l-leg ladder system is gapless or gapful for an odd or even Nt, respectively.