Localization of spinons in random Majumdar-Ghosh chains

TL;DR

This paper investigates how disorder affects spinon excitations in frustrated dimerized spin chains at the Majumdar-Ghosh point, revealing two distinct localization mechanisms and a disorder-induced phase transition.

Contribution

It identifies and characterizes two localization mechanisms for spinons in disordered Majumdar-Ghosh chains, including an Anderson localization and a random confinement process, and analyzes their effects.

Findings

Spinons localize in Lifshitz states with analytically derived localization length.

A quantum phase transition occurs at the RMG point with increasing disorder.

Disorder induces a gapless, partially polarized phase via random confinement.

Abstract

We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh (RMG) point. There, spinons are almost independent, remain gapped, and localize in Lifshitz states whose localization length is analytically obtained. The RMG point then displays a quantum phase transition to phase of localized spinons at large disorder. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.