Abstract
Using the bosonization and level spectroscopy methods, we study the ground-state phase diagram of a X X Z antiferromagnet on a railroad–trestle lattice with asymmetric leg interactions. It is shown that the asymmetry does not change the dimer/Néel transition line significantly, which agrees with the expectation based on a naive bosonization procedure, but it does change the dimer/spin-fluid transition line. To understand this observation, we analyze eigenvectors of the ground state, dimer excitation, doublet excitation and Néel excitation, and find that only the doublet excitation is affected by the asymmetric interaction.
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