Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain

TL;DR

This study uses DMRG calculations to map the phase diagram of a disordered S=1 antiferromagnetic Heisenberg chain, identifying transitions between the Haldane and random singlet phases influenced by disorder strength.

Contribution

It provides a detailed analysis of disorder effects on the S=1 chain, revealing phase transitions and critical behavior using numerical simulations.

Findings

Weak disorder maintains the Haldane phase with a disorder-dependent dynamical exponent.

Strong disorder induces a transition to the random singlet phase with diverging dynamical exponent.

Distinct singularities characterize the phases and the critical point.

Abstract

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S=1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function, and the string order parameter. For this distribution at weak disorder, the systems is in the gapless Haldane phase with a disorder dependent dynamical exponent, z, and z=1 signals, the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.