Correlations in Quantum Spin Ladders with Site and Bond Dilution
Abstract
We investigate the effects of quenched disorder, in the form of site and bond
dilution, on the physics of the $S=1/2$ antiferromagnetic Heisenberg model on
even-leg ladders. Site dilution is found to prune rung singlets and thus create
localized moments which interact via a random, unfrustrated network of
effective couplings, realizing a random-exchange Heisenberg model (REHM) in one
spatial dimension. This system exhibits a power-law diverging correlation
length as the temperature decreases. Contrary to previous claims, we observe
that the scaling exponent is non-universal, i.e., doping dependent. This
finding can be explained by the discrete nature of the values taken by the
effective exchange couplings in the doped ladder. Bond dilution on even-leg
ladders leads to a more complex evolution with doping of correlations, which
are weakly enhanced in 2-leg ladders, and are even suppressed for low dilution
in the case of 4-leg and 6-leg ladders. We clarify the different aspects of
correlation enhancement and suppression due to bond dilution by isolating the
contributions of rung-bond dilution and leg-bond dilution.