Comment on ``Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets"

TL;DR

This paper critiques a previous study claiming the Haldane phase's stability against all bond randomness in spin chains, providing a more nuanced analysis and estimating the critical randomness where phase transition occurs.

Contribution

It clarifies the limitations of prior numerical results and offers a semiquantitative estimate of the critical randomness for phase transition in disordered spin chains.

Findings

Previous results do not cover the broadest randomness distributions.

The critical randomness for phase transition is estimated.

The Haldane phase's stability is limited to certain randomness types.

Abstract

In a recent Letter (PRL 83, 3297 (1999)), Hida presented numerical results indicating that the Haldane phase of the Heisenberg antiferromagnetic spin-1 chain is stable against bond randomness, for box distributions of the bond strength, even when the box distribution stretches to zero bond strength. The author thus concluded that the Haldane phase is stable against bond randomness for any distribution of the bond strength, no matter how broad. In this Comment, we (i) point out that the randomness distributions studied in this Letter do not represent the broadest possible distributions, and therefore these numerical results do not lead to the conclusion that the Haldane phase is stable against any randomness; and (ii) provide a semiquantitative estimate of the critical randomness beyond which the Haldane phase yields to the Random Singlet phase, in a specific class of random distribution functions for the bond strength.