Time Crystals in the Driven Transverse Field Ising Model under Quasiperiodic Modulation

TL;DR

This paper explores the emergence of time crystals in a driven transverse field Ising model with quasiperiodic modulation, revealing localized excitations, spectral pairing, and eigenstate order through analytical and numerical methods.

Contribution

It introduces a novel driven Ising model with quasiperiodic modulation, demonstrating the existence of time crystals via analytical phase boundary analysis and numerical localization studies.

Findings

Existence of Majorana edge modes in the driven model

Localization of single-particle excitations in certain parameter regions

Eigenstate order and spectral pairing indicative of time crystals

Abstract

We investigate the transverse field Ising model subject to a two-step periodic driving protocol and quasiperiodic modulation of the Ising couplings. Analytical results on the phase boundaries associated with Majorana edge modes and numerical results on the localization of single-particle excitations are presented. The implication of a region with fully localized domain-wall-like excitations in the parameter space is eigenstate order and exact spectral pairing of Floquet eigenstates, based on which we conclude the existence of time crystals. We also examine various correlation functions of the time crystal phase numerically, in support of its existence.