Ground state and excitation of an asymmetric spin ladder model

We perform a systematic investigation on an asymmetric zigzag spin ladder with interleg exchange J 1 and different exchange integrals J 2 ′δ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gordon model by using bosonization. Renormalization-group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing J 2 =J 1 /2, we find, as a function of δ, a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange δ, the gap size of excitations is found to decrease with increasing δ. We also extend our study to a two-dimensional double layer model with an exactly known ground state.

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