Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains

TL;DR

This paper explores a long-range XYZ spin model that can be tuned to exhibit both continuous time crystal behavior and quantum many-body scars, revealing their coexistence and differences through numerical simulations.

Contribution

It introduces a novel long-range XYZ spin model that encompasses both continuous time crystal and quantum many-body scar phases, enabling tuning between these phenomena.

Findings

Identified a regime where CTC and QMBS coexist.

Mapped the dynamical phase diagram using numerical methods.

Discussed experimental protocols to distinguish CTC and QMBS.

Abstract

Persistent oscillatory dynamics in non-equilibrium many-body systems is a tantalizing manifestation of ergodicity breakdown that continues to attract much attention. Recent works have focused on two classes of such systems: discrete time crystals and quantum many-body scars (QMBS). While both systems host oscillatory dynamics, its origin is expected to be fundamentally different: discrete time crystal is a phase of matter which spontaneously breaks the $\mathbb{Z}_2$ symmetry of the external periodic drive, while QMBS span a subspace of non-thermalizing eigenstates forming an su(2) algebra representation. Here we ask a basic question: is there a physical system that allows to tune between these two dynamical phenomena? In contrast to much previous work, we investigate the possibility of a \emph{continuous} time crystal (CTC) in undriven, energy-conserving systems exhibiting prethermalization. We introduce a long-range XYZ spin model and show that it encompasses both a CTC phase as well as QMBS. We map out the dynamical phase diagram using numerical simulations based on exact diagonalization and time-dependent variational principle in the thermodynamic limit. We identify a regime where QMBS and CTC order co-exist, and we discuss experimental protocols that reveal their similarities as well as key differences.