Single-particle localization in a two-dimensional Rydberg spin system

TL;DR

This paper investigates how excitation transport and localization phenomena occur in a two-dimensional Rydberg spin system with tunable disorder, revealing localized, delocalized, and multifractal eigenstates and discussing experimental observability.

Contribution

It provides a detailed analysis of localization and eigenstate properties in a 2D Rydberg spin system, highlighting the effects of disorder and system size on localization.

Findings

Localized eigenstates dominate at strong disorder.

Eigenstates become delocalized as disorder weakens.

In the infinite-size limit, all states are ultimately localized.

Abstract

We study excitation transport in a two-dimensional system of randomly assembled spins with power-law hopping in two dimensions. This model can be realized in cold atom quantum simulators with Rydberg atoms. In these experiments, due to the Rydberg blockade effect, the degree of disorder in the system is effectively tunable by varying the spin density. We study dynamics and eigenstate properties of the model as a function of disorder strength and system size and discuss potential limitations for experiments. At strong disorder we predominantly observe localized eigenstates with power-law tails. In this regime the spectral and eigenstate properties can be understood in a perturbative picture of states localized on small clusters of spins. As the disorder strength is weakened eigenstates become increasingly delocalized and a set of seemingly multifractal states appears in the low-energy tail of the spectrum. A detailed study of the system-size scaling of the eigenstate properties indicates that in the infinite-size limit all states eventually become localized. We discuss the feasibility of observing localization effects experimentally in the spatial spreading of an initially localized excitation and identify limited system sizes and finite decoherence rates as major challenges. Our study paves the way towards an experimental observation of localization effects in Rydberg spin systems with tunable disorder.