Quantum walk on a graph of spins: magnetism and 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).

Disorder-free localization in quantum walks

“…We have studied disorder-free localization of a quantum walker coupled to local spins on a one-dimensional lattice. Similar to models of quantum walks on graphs coupled to spins living on nodes 36 or links 38 , the local spins in our model live on lattice sites and do not act on the coin. The Hamiltonian and the initial spin state we have chosen are translationally invariant, yet localization occurs merely due to the interactions between the walker and the local spins.…”

“…In general, even after starting with a product state at t = 0, it is impossible to factorize any degree of freedom completely at later times. At this point, it is worthy to note that the model we consider here is actually simpler in terms of its construction compared to the other similar models since we consider a one-dimensional position space and the spins have no direct action on the walker [36][37][38] .…”