Comment on "Disorder Induced Quantum Phase Transition in Random-Exchange Spin-1/2 Chains"

TL;DR

This paper analyzes the effects of weak disorder on random antiferromagnetic spin-1/2 chains, clarifying the existence of a crossover length scale that influences the interpretation of previous numerical results regarding the infinite randomness fixed point.

Contribution

It demonstrates that previous DMRG studies did not reach the asymptotic regime and provides a scaling form for the spin-correlation function consistent with the IRFP scenario.

Findings

Crossover length scale x_W diverges as disorder weakens.

Previous numerical data are not in the asymptotic regime due to system size limitations.

A new scaling form for spin correlations aligns with the IRFP and random singlet phase.

Abstract

We reconsider the random bond antiferromagnetic spin-1/2 chain for weak disorder and demonstrate the existence of crossover length scale x_W that diverges with decreasing strength of the disorder. Recent DMRG calculations [Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found evidence for a non-universal behavior in this model and found no indications of a universal infinite randomness fixed point (IRFP) scenario. We show that these data are not in the asymptotic regime since the system sizes that have been considered are of the same order of magnitude or much smaller than the crossover length x_W. We give a scaling form for the xx-spin-correlation function that takes this crossover length into account and that is compatible with the IRFP scenario and a random singlet phase.