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

Abstract

We study a 1D system with a power-law quasiparticle dispersion $\propto |k|^α\sign k$ 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.

4+ pages, 2 figures

References in corpus (5)

• Anderson Transitions
• Electron transport in disordered graphene
• Effect of Disorder on Transport in Graphene
• Rare region effects dominate weakly disordered 3D Dirac points
• Unconventional localisation transition in high dimensions

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