Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires

TL;DR

This paper investigates how long-range power-law interactions influence correlation decay and localization in disordered one-dimensional quantum systems, revealing algebraic decay patterns regardless of disorder strength.

Contribution

It demonstrates that power-law interactions cause algebraic decay of correlations and wave-functions in disordered phases, a novel insight contrasting short-range model expectations.

Findings

Correlation functions decay algebraically with distance for all interaction exponents.

Wave-functions exhibit similar algebraic localization.

Decay exponents depend only on the interaction decay parameter lpha.

Abstract

We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance $\ell$ as a power-law $1/\ell^\alpha$. Using a combination of analytical and numerical results, we demonstrate that power-law interactions imply a long-distance algebraic decay of correlations within disordered-localized phases, for all exponents $\alpha$. The exponent of algebraic decay depends only on $\alpha$, and not, e.g., on the strength of disorder. We find a similar algebraic localization for wave-functions. These results are in contrast to expectations from short-range models and are of direct relevance for a variety of quantum mechanical systems in atomic, molecular and solid-state physics.