Gauge theory description of spin ladders

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Abstract
An 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 when the inter-chain Heisenberg coupling is small compared with the intra-chain Heisenberg coupling. It is also shown that a cyclically symmetric -leg ladder system is gapless or gapful for an odd or even , respectively.