Quantum Levy flights and multifractality of dipolar excitations in a random system

TL;DR

This paper investigates how dipolar excitations propagate in disordered systems, revealing localization in 1D and 2D, and ergodic versus non-ergodic states in 3D, with implications for understanding quantum transport and multifractality.

Contribution

It provides a detailed analysis of Levy flights and multifractality in dipolar systems across different dimensions, highlighting ergodic transitions related to lattice filling.

Findings

All states are localized in 1D and 2D, with large localization lengths in 2D.

In 3D, states are extended but can be non-ergodic, with energy-dependent ergodic regions.

Reducing lattice filling induces a transition from ergodic to non-ergodic behavior.

Abstract

We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). We analyze the eigen-energy spectra and the multifractal structure of the wavefunctions. In 1D and 2D all states are localized, although in 2D the localization length can be extremely large leading to an effective localization-delocalization crossover in realistic systems. In 3D all eigenstates are extended but not always ergodic, and we identify the energy intervals of ergodic and non-ergodic states. The reduction of the lattice filling induces an ergodic to non-ergodic transition, and the excitations are mostly non-ergodic at low filling.