Interacting quantum walk on a graph

TL;DR

This paper introduces a quantum system with spins and a hopping particle on a graph, studying its relaxation to equilibrium states and linking it to eigenvector thermalization, random matrix theory, and entanglement.

Contribution

It presents a new model of interacting quantum walks on graphs, analyzing relaxation dynamics and their connection to thermalization and entanglement.

Findings

System relaxes to paramagnetic or ferromagnetic states

Eigenvector thermalization is observed

System exhibits random matrix statistics

Abstract

We introduce an elementary quantum system consisting of a set of spins on a graph and a particle hopping between its nodes. The quantum state is build sequentially, applying a unitary transformation that couples neighboring spins and, at a node, the local spin with the particle. We observe the relaxation of the system towards a stationary paramagnetic or ferromagnetic state, and demonstrate that it is related to eigenvectors thermalization and random matrix statistics. The relation between these macroscopic properties and interaction generated entanglement is discussed.