Disorder-driven transition in a chain with power-law hopping

TL;DR

This paper investigates a one-dimensional system with power-law dispersion under disorder, revealing a quantum phase transition characterized by critical behavior similar to high-dimensional localization phenomena, confirmed through numerical simulations.

Contribution

It demonstrates a disorder-driven quantum phase transition in a 1D system with power-law dispersion for the first time, linking it to high-dimensional localization effects and providing a platform for further studies.

Findings

Existence of a disorder-driven transition for α<1/2

Critical exponents and disorder strength depend on α

Potential for experimental realization in ultracold atom chains

Abstract

We study a 1D system with a power-law quasiparticle dispersion $\propto |k|^\alpha\sign k$ in the presence of a short-range-correlated random potential and demonstrate that for $\alpha<1/2$ it exhibits a disorder-driven quantum phase transition with the critical properties similar to those of the localisation transition near the edge of the band of a semiconductor in high dimensions, studied in Refs. 1 and 2. Despite the absence of localisation in the considered 1D system, the disorder-driven transition manifests itself, for example, in a critical form of the disorder-averaged density of states. We confirm the existence of the transition by numerical simulations and find the critical exponents and the critical disorder strength as a function of $\alpha$. The proposed system thus presents a convenient platform for numerical studies of the recently predicted unconventional high-dimensional localisation effects and has the potential for experimental realisations in chains of ultracold atoms in optical traps.