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arXiv · 1504.05971

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

M. Garttner·S. V. Syzranov·A. M. Rey·V. Gurarie·L. Radzihovsky
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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 $α<1/2$ 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 $α$. 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.

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M. Garttner, S. V. Syzranov, A. M. Rey, V. Gurarie, L. Radzihovsky. 2015-08-17. Disorder-driven transition in a chain with power-law hopping. https://doi.org/10.1103/physrevb.92.041406

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