Quantum walk on a graph of spins: magnetism and entanglement

TL;DR

This paper introduces a quantum walk model on a graph with spins on edges, exploring its magnetic and entanglement properties, revealing complex dynamics including localization, spin oscillations, and volume-law entanglement.

Contribution

The paper presents a novel quantum walk model with particle-spin interactions on a graph, connecting it to Landau-Lifshitz dynamics and analyzing its entanglement and magnetic behaviors.

Findings

Rich dynamical regimes including propagation and localization.

Spin oscillations and relaxation observed in the model.

Asymptotic states exhibit volume-law entanglement.

Abstract

We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a one dimensional lattice, to investigate its magnetic and entanglement properties. In the continuum limit, we recover a Landau-Lifshitz equation that describes the precession of spins. A rich dynamics is observed, with regimes of particle propagation and localization, together with spin oscillations and relaxation. Entanglement of the asymptotic states follows a volume law for most parameters (the coin rotation angle and the particle-spin coupling).