Discrete time crystal in the gradient field Heisenberg model

TL;DR

This paper demonstrates that discrete time crystal phases can exist in a Heisenberg spin chain with a magnetic field gradient, expanding the understanding of non-ergodic phases beyond disorder-based localization.

Contribution

It shows that time crystal phases occur in gradient field systems, not just disordered systems, and provides numerical evidence for their realization in quantum dot spin arrays.

Findings

Time crystalline order persists over broad parameter ranges.

Long-time spin expectation values are preserved.

Mutual information indicates non-ergodic phases.

Abstract

We show that time crystal phases, which are known to exist for disorder-based many-body localized systems, also appear in systems where localization is due to strong magnetic field gradients. Specifically, we study a finite Heisenberg spin chain in the presence of a gradient field, which can be realized experimentally in quantum dot systems using micromagnets or nuclear spin polarization. Our numerical simulations reveal time crystalline order over a broad range of realistic quantum dot parameters, as evidenced by the long-time preservation of spin expectation values and the asymptotic form of the mutual information. We also consider the undriven system and present several diagnostics for many-body localization that are complementary to those recently studied. Our results show that these non-ergodic phases should be realizable in modest-sized quantum dot spin arrays using only demonstrated experimental capabilities.