Correlations in Quantum Spin Ladders with Site and Bond Dilution

TL;DR

This paper studies how site and bond dilution affect quantum spin ladders, revealing non-universal scaling behavior and complex correlation changes, with implications for understanding disordered quantum magnetic systems.

Contribution

It demonstrates that doping-dependent scaling exponents in diluted ladders are due to the discrete exchange couplings, and clarifies the effects of bond dilution on correlations across different ladder geometries.

Findings

Site dilution creates localized moments and a random-exchange Heisenberg model.

Scaling exponent varies with doping, indicating non-universality.

Bond dilution effects differ between 2-leg and higher-leg ladders.

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.