Hilbert Space Fragmentation and Subspace Scar Time-Crystallinity in Driven Homogeneous Central-Spin Models

We study the stroboscopic non-equilibrium quantum dynamics of periodically kicked Hamiltonians involving homogeneous central-spin interactions. The system exhibits a strong fragmentation of Hilbert space into four-dimensional Floquet-Krylov subspaces, which oscillate between two disjointed two-dimen...

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Bibliographic Details
Published inarXiv.org
Main Authors Kumar, Abhishek, Frantzeskakis, Rafail, Barnes, Edwin
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.02.2024
Subjects
Color centers
Eigenvectors
Fragmentation
Hamiltonian functions
Hilbert space
Ising model
Period doubling
Phase diagrams
Quantum dots
Rare earth elements
Robustness (mathematics)
Subspaces
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Summary:We study the stroboscopic non-equilibrium quantum dynamics of periodically kicked Hamiltonians involving homogeneous central-spin interactions. The system exhibits a strong fragmentation of Hilbert space into four-dimensional Floquet-Krylov subspaces, which oscillate between two disjointed two-dimensional subspaces and thus break the discrete time-translation symmetry of the system. Our analytical and numerical analyses reveal that fully polarized states of the satellite spins exhibit fragmentations that are stable against perturbations and have high overlap with Floquet eigenstates of atypically low bipartite entanglement entropy (scar states). We present evidence of robust time-crystalline behavior in the form of a period doubling of the total magnetization of fully polarized satellite spin states that persists over long time scales. We compute non-equilibrium phase diagrams with respect to a magnetic field, coupling terms, and pulse error for various interaction types, including Heisenberg, Ising, XXZ, and XX. We also discuss possible experimental realizations of scar time crystals in color center, quantum dot, and rare-earth ion platforms.
ISSN:2331-8422