Time-crystalline behavior in an engineered spin chain

Abstract

Time crystals appear when systems display a commensurate spontaneous breaking of the discrete time translational invariance imposed by an external periodic drive. No consensus on the definition has been reached as yet, but important aspects comprise robustness against small variations of the parameters and the initial quantum state. Often, disorder and interaction are thought to be essential ingredients for the occurrence of time crystals. We study a finite-length polarized XX spin chain engineered to display a spectrum of equidistant energy levels without drive and show that it keeps a spectrum of equidistant quasienergies in Floquet theory for a large variety of periodic driving schemes. This interesting behavior is explained by mapping the XX spin chain with $N+1$ sites to a single large spin with $S=N/2$ invoking the closure of the group SU(2). For suitably tuned parameters this system realizes time crystals of various periodicities for \emph{all} initial states. The robustness against variations of the parameters is also discussed. Thereby, we establish a clean system without interaction which can display the phenomenon of time crystallization.

17 pages, 5 figures. Title changed. Extended discussion of disorder effects. Accepted for publication in Phys. Rev. B

References in corpus (8)

• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Absence of Quantum Time Crystals
• Mirror Inversion of Quantum States in Linear Registers
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• Electron wavepacket propagation and entanglement in a chain of coupled quantum dots
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Cited by in corpus (7)

• Systematic construction of scarred many-body dynamics in 1D lattice models
• Classical Stochastic Discrete Time Crystals
• Homogeneous Floquet time crystal protected by gauge invariance
• Homogeneous Floquet time crystal from weak ergodicity breaking
• Polynomial filter diagonalization of large Floquet unitary operators
• Time Crystals in the Driven Transverse Field Ising Model under Quasiperiodic Modulation
• Discrete time crystal order in spin chains enabled by Floquet flat bands