Quantum Transport in Disordered Spin Networks: Emergent Timescales and Competing Pathways

TL;DR

This paper investigates how geometric heterogeneity and hierarchical couplings in disordered spin networks lead to multiple, distinct transport timescales, affecting relaxation dynamics and energy transfer.

Contribution

It reveals the physical origin of long relaxation times due to internal hybridization and effective detuning in disordered spin networks, supported by models and simulations.

Findings

Hierarchical couplings cause separation of dynamical timescales.

Strong internal hybridization creates effective detuning, prolonging relaxation.

Disordered spin configurations exhibit orders-of-magnitude slower relaxation.

Abstract

Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.