Disorder-free localization in quantum walks

TL;DR

This paper demonstrates disorder-free localization in a quantum walk system where internal interactions cause localization without any disorder, revealing slow entanglement growth even in delocalized regimes.

Contribution

It introduces a model of a quantum walk with on-site spin interactions that cause localization without disorder, and analyzes its dynamics and entanglement properties.

Findings

Weak interactions lead to subdiffusive spread with ballistic tails.

Strong interactions cause exponential localization of the quantum walker.

Entanglement growth is slow even in the delocalized regime.

Abstract

The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time quantum walker which exhibits disorder free localization. The quantum walker moves on a one-dimensional lattice and interacts with on-site spins by coherently rotating them around a given axis at each step. Since the spins do not have dynamics of their own, the system poses the local spin components along the rotation axis as an extensive number of conserved moments. When the interaction is weak, the spread of the walker shows subdiffusive behaviour having downscaled ballistic tails in the evolving probability distribution at intermediate time scales. However, as the interaction gets stronger the walker gets exponentially localized in the complete absence of disorder in both lattice and initial state. Using a matrix-product-state ansatz, we investigate the relaxation and entanglement dynamics of the on-site spins due to their coupling with the quantum walker. Surprisingly, we find that even in the delocalized regime, entanglement growth and relaxation occur slowly unlike marjority of the other models displaying a localization transition.