Perturbation theory for spin ladders using angular-momentum coupled bases

We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schrodinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic 2x12 ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is lambda(c)similar or equal to 0.8, with lambda defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of lambda(c)similar or equal to 1.25. Thus, we conclude that the plaquette: basis offers the best currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic (lambda = 1) spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation. [S0163-1829(98)08238-1].