Dynamical properties of the Haldane chain with bond disorder

TL;DR

This study investigates how bond disorder affects the dynamical properties of the S=1 antiferromagnetic Heisenberg chain, revealing a transition from Haldane gap to a random-singlet phase with distinct low-energy excitations.

Contribution

It provides a detailed analysis of the disorder-induced transition in the Haldane chain using numerical methods, identifying the nature of low-energy excitations and domain structures.

Findings

Haldane gap closes at disorder strength ~0.5

System enters a random-singlet phase at disorder >1

Presence of effective spin-1/2 and spin-1 domains contributing to low-energy excitations

Abstract

By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the $S=1$ antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at $\delta_{\Delta}\sim 0.5$ with more and more low-energy excitations coming out. After the critical disorder strength $\delta_c\sim 1$, the system reaches a random-singlet phase with prominent sharp peak at $\omega=0$ and broad continuum at $\omega>0$ of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These "spins" can form the weakly coupled long-range singlets due to quantum fluctuation which contribute to the sharp peak at $\omega=0$.