The time crystal phase emerges from the qubit network under unitary random operations

TL;DR

This paper demonstrates the emergence of a time crystal phase in a fully connected qubit network under random unitary evolution, showing robustness to noise and extending understanding of non-stationary phases in open quantum systems.

Contribution

It introduces a novel open quantum system model where a time crystal phase emerges from random unitary dynamics with environmental effects, supported by theoretical and numerical analysis.

Findings

Non-stationary oscillatory states encode initial state memory

Time crystal phase is robust to various noise types

The phenomenon is widespread across different Hamiltonians

Abstract

In this paper, we report findings of non-stationary behavior observed in a fully connected qubit network, utilizing a random unitary evolution model in open quantum system theory. The environmental effect is reflected in the partial swap (PSW) interaction between pairs of qubits with a certain probability. Our study begins with a simple Ising-type Hamiltonian and through many iterations of random unitary evolution, a non-stationary oscillatory state may arise, which encodes certain memory of the initial state. The non-trivial periodic motion of some local observables is indicative of a continuous time crystal phase. We also explore the extension of our study to other types of Hamiltonians and demonstrate that this non-stationary behavior is widespread in our model due to the generalized dynamical symmetry. Remarkably, both theoretical and numerical analysis support the robustness of the constructed time crystal phase to most types of noise. Our research provides a new perspective for constructing the time crystal phase in an open system model.