Localization and critical diffusion of quantum dipoles in two dimensions

TL;DR

This paper investigates the unique localization behavior of quantum dipoles in two dimensions, revealing persistent critical states due to long-range hops and a possible transition between diffusion regimes.

Contribution

It introduces a modified non-linear supermatrix sigma-model to analyze quantum dipole propagation, highlighting the existence of scale-independent critical wavefunctions and phase transitions.

Findings

Critical wavefunctions exist for all parameters in T-invariant systems.

System exhibits a transition between ordinary diffusion and Levy-flights.

Diffusion constant can logarithmically increase with scale in certain regimes.

Abstract

We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to existence of long range hops. We found that the critical wavefunctions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T-invariant the states are critical for all values of the parameters. Otherwise, there can be a "metal-insulator" transition between this "ordinary" diffusion and the Levy-flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified non-linear supermatrix $\sigma$-model.