Phases of random antiferromagnetic spin-1 chains

TL;DR

This paper develops a real-space renormalization method to analyze how bond randomness affects the phases of antiferromagnetic spin-1 chains, revealing different phases and bond distributions.

Contribution

It introduces a numerical decimation scheme and detailed probability distribution analysis for bonds in disordered spin-1 chains, extending understanding of phase behavior under randomness.

Findings

Identification of four bond types during renormalization

Probability distributions of bonds vary with disorder strength

Confirmation of the random singlet phase in strong disorder regime

Abstract

We formulate a real-space renormalization scheme that allows the study of the effects of bond randomness in the Heisenberg antiferromagnetic spin-1 chain. There are four types of bonds that appear during the renormalization flow. We implement numerically the decimation procedure. We give a detailed study of the probability distributions of all these bonds in the phases that occur when the strength of the disorder is varied. Approximate flow equations are obtained in the weak-disorder regime as well as in the strong disorder case where the physics is that of the random singlet phase.