Effects of critical correlations on quantum percolation in two dimensions

TL;DR

This study investigates how classical magnetic phase transitions influence quantum particle localization in a two-dimensional system with correlated disorder, revealing potential delocalization effects near the transition.

Contribution

It introduces a model linking classical Ising transitions to quantum percolation, highlighting the impact of correlations on quantum localization phenomena.

Findings

Classical phase transition can induce a quantum delocalization-localization transition.

Ising correlations suppress compact localized eigenstates.

Long-range correlations affect quantum energy level statistics and wave dynamics.

Abstract

We analyze the out-of-equilibrium dynamics of a quantum particle coupled to local magnetic degrees of freedom that undergo a classical phase transition. Specifically, we consider a two-dimensional tight-binding model that interacts with a background of classical spins in thermal equilibrium, which are subject to Ising interactions and act as emergent, correlated disorder for the quantum particle. Particular attention is devoted to temperatures close to the ferromagnet-to-paramagnet transition. To capture the salient features of the classical transition, namely the effects of long-range correlations, we focus on the strong coupling limit, in which the model can be mapped onto a quantum percolation problem on spin clusters generated by the Ising model. By inspecting several dynamical probes such as energy level statistics, inverse participation ratios, and wave-packet dynamics, we provide evidence that the classical phase transition might induce a delocalization-localization transition in the quantum system at certain energies. We also identify further important features due to the presence of Ising correlations, such as the suppression of compact localized eigenstates.