Interacting quantum walk on a graph

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.

15 pages, 11 figures (v2 extended version)

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Cited by in corpus (6)

• Disorder-free localization in quantum walks
• Entanglement dynamics and phase transitions of the Floquet cluster spin chain
• Quantum walk on a graph of spins: magnetism and entanglement
• Thermal state entanglement entropy on a quantum graph
• Robustness of Aharonov-Bohm cages in quantum walks
• Geodesic Quantum Walks