Numerical Analysis of the Bond-Random Antiferromagnetic S=1 Heisenberg Chain

TL;DR

This study uses exact diagonalization and finite-size scaling to show that the Haldane phase in a bond-random S=1 Heisenberg chain remains stable against randomness, contradicting some analytic predictions of a phase transition.

Contribution

It provides numerical evidence that the Haldane phase persists under randomness, challenging existing analytic theories predicting a phase transition.

Findings

Haldane phase remains stable against randomness

Magnetic correlation length is unaffected in the Haldane phase

No phase transition observed until extremely broad bond distribution

Abstract

Ground state of the bond-random antiferromagnetic S=1 Heisenberg chain with the biquadratic interaction -\beta\sum_i(S_i S_i+1)^2 is investigated by means of the exact-diagonalization method and the finite-size-scaling analysis. It is shown that the Haldane phase \beta\sim0 persists against the randomness; namely, no randomness-driven phase transition is observed until at a point of extremely-broad-bond distribution. We found that in the Haldane phase, the magnetic correlation length is kept hardly changed. These results are contrastive to those of an analytic theory which predicts a second-order phase transition between the Haldane and the random-singlet phases at a certain critical randomness.