Quantum Monte Carlo study of weakly coupled spin ladders

We report a quantum Monte Carlo study of the thermodynamic properties of arrays of spin ladders with various widths (n), coupled via a weak interladder exchange coupling {alpha}J, where {ital J} is the intraladder coupling both along and between the chains. This coupled ladder system serves as a simplified model for the magnetism of presumed ordered spin and charge stripes in the two-dimensional CuO{sub 2} planes of hole-doped copper oxides. Our results for n=3 with weak interladder coupling {alpha}=0.05, estimated from the t-t{sup {prime}}-t{sup {double_prime}}-J model, show good agreement with the ordering temperature of the recently observed spin-density-wave condensation in La{sub 2}CuO{sub 4+y}. We show that there exists a quantum critical point at {alpha}{sub c}{approx_equal}0.07 for n=4, and determine the phase diagram. Our data at this quantum critical point agree quantitatively with the universal scaling predicted by the quantum nonlinear {sigma} model. We also report results on random mixtures of n=2 and n=3 ladders, which correspond to the doping region near but above 1/8. Our study of the magnetic static structure factor reveals a saturation of the incommensurability of the spin correlations around 1/8, while the incommensurability of the charge stripes grows linearly with hole concentration. The implications of this result for the interpretation of neutron-scattering experiments on the dynamic spin fluctuations in La{sub 2{minus}x}Sr{sub x}CuO{sub 4} are discussed. {copyright} {ital 1999} {ital The American Physical Society}