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arXiv:cond-mat/9709297 · Physical review. B, Condensed matter

Weakly disordered spin ladders

E. Orignac, Thierry Giamarchi

Published Mar 1, 1998• 54 citations
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Abstract

We analyze an anisotropic spin-1/2 two-leg ladder in the presence of various types of random perturbations. The generic phase diagram for the pure system, in a way similar to spin one chains, consists of four phases: an antiferromagnet, a Haldane gap or a singlet phase (depending on the sign of interchain coupling), and two $\mathrm{XY}$ phases designated by $\mathrm{XY}1$ and $\mathrm{XY}2$. The effects of disorder depend crucially on whether it preserves $\mathrm{XY}$ symmetry (random field along $z$ and random exchange) or not (random anisotropy or random $\mathrm{XY}$ fields). In all cases we computed the new phase diagram and the correlation length for the disordered system. The ladder exhibits a remarkable stability to disorder with $\mathrm{XY}$ symmetry. Not only the singlet phases but also the massless $\mathrm{XY}1$ phase are totally unaffected by disorder in stark contrast with the single chain case. Even in the presence of an external magnetic field breaking the spin gap most of the phase diagram (including the $\mathrm{XY}$ point) remains unaffected by the disorder, again in opposition with the single chain case. This stabilization towards disorder is similar, albeit stronger, to the one occurring for fermionic ladders. On the other hand, the $\mathrm{XY}2$ phase is very strongly suppressed. Disorder breaking $\mathrm{XY}$ symmetry has much stronger effects and most of the phases at the exception of the singlet one are now destroyed. Interestingly, the disordered $\mathrm{XY}1$ phase has a much shorter correlation length than the disordered $\mathrm{XY}2$ phase contrarily with the case of perturbations preserving the rotation symmetry around the $z$ axis. The ladder system is thus in fact much more anisotropic than its single chain counterpart with identical exchanges. Finally we examine the case of strong disorder or weak interchain exchange for $\mathrm{XY}$ symmetric disorder. Close to the isotropic point, when the interchain exchange is increased the system undergoes a transition between two decoupled disordered spin-1/2 chains to a singlet ladder unaffected by disorder. For more $\mathrm{XY}$ like systems, the transition occurs in two steps with a nondisordered $\mathrm{XY}1$ phase occurring between the decoupled chains and the singlet phase. Comparison with other disordered gapped systems such as spin one chains is discussed.

DOI
10.1103/physrevb.57.5812

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