Effects of impurities in spin Bose-metal phase on a two-leg triangular strip

We study the effects of nonmagnetic impurities in a spin Bose-metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Sheng et al., arXiv:0902.4210). This phase is a quasi-one-dimensional (quasi-1D) descendant of a two-dimensional (2D) spin liquid with spinon Fermi sea and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local-energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near the defect, both of which can be measured in experiments. The spin Bose metal has dominant correlations at characteristic incommensurate wave vectors that are revealed near the defect. Thus, the bond energy shows a static texture oscillating as a function of distance from the defect and decaying as a slow power law. The local spin susceptibility also oscillates and actually increases as a function of distance from the defect, similar to the effect found in the 1D chain [S. Eggert and I. Affleck, Phys. Rev. Lett. 75, 934 (1995)]. We calculate the corresponding power-law exponents for the textures as a function of one Luttinger parameter of the SBM theory.

Figure 1

(Color online) The top figure represents the original two-leg triangular ladder model with ring exchanges and the thick lines represent the defects due to the impurities. The bottom figures represent the corresponding defects in the equivalent 1D model (Ref. 8). (1) represents the defect symmetric with respect to a bond center, while (2), (3), and (4) represent defects symmetric about a site of the 1D chain. In general, different impurities will lead to different fixed points. Impurity (1) is likely to lead to a fixed point with decoupled semi-infinite systems and a nonmagnetic cluster containing an even number of sites, while impurities (2), (3), and (4) is likely to lead to a fixed point with decoupled semi-infinite systems and an effective spin formed by a cluster with an odd number of sites.