Quantum walkers in a disordered lattice with power-law hopping

TL;DR

This study investigates how long-range hopping and interactions influence quantum walks of bosons in disordered lattices, revealing complex localization and transport behaviors with potential experimental relevance.

Contribution

It provides a detailed phase diagram analysis of single and two-particle quantum walks under power-law hopping and disorder, highlighting novel transport regimes and the impact of interactions.

Findings

Localization and extended regimes depend on disorder and hopping parameters.

Disorder can enhance diffusion in interacting two-particle systems.

Interactions and short-range tunneling can constrain space and modify transport.

Abstract

We study the effects of interparticle interactions and power-law tunneling couplings on quantum walks executed by both a single one and a pair of hard-core bosons moving in clean and disordered one-dimensional lattices. For this purpose, we perform exact diagonalization to explicitly evaluate the short and long time probabilities of finding the walkers within a surveillance area. Our main conclusions, summarized in phase diagrams in the disorder-power-law and interaction-disorder spaces, allowed us to discern two different scenarios for the single and two quantum walkers dynamics. While in the single particle case the transition to localized and extended regimes is identified for well defined values of the disorder amplitude and power law hopping, those frontiers are replaced by diffuse contours in the interacting two particle case. In fact, counterintuitive transport regimes as diffusion enhanced by disorder, and space constrained dynamics assisted by both interactions and short tunneling range are found. Our results are of direct relevance for quantum systems with long-range interactions that are currently realized in the laboratory.