Subspace-thermal discrete time crystals from phase transitions between different n-tuple discrete time crystals

• URL: http://arxiv.org/abs/2409.02848v3
• Date: Thu, 3 Oct 2024 22:49:40 GMT
• Title: Subspace-thermal discrete time crystals from phase transitions between different n-tuple discrete time crystals
• Authors: Hongye Yu, Tzu-Chieh Wei,
• Abstract summary: We propose a new Floquet time crystal model that responds in arbitrary multiples of the driving period. Transitions between these time crystals with different periods give rise to a novel phase of matter that we call subspace-thermal discrete time crystals.
• Score: 0.46040036610482665
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new Floquet time crystal model that responds in arbitrary multiples of the driving period. Such an $n$-tuple discrete time crystal is theoretically constructed by permuting spins in a disordered chain and is well suited for experiment implementations. Transitions between these time crystals with different periods give rise to a novel phase of matter that we call subspace-thermal discrete time crystals, where states within subspaces are fully thermalized at an early time. However, the whole system still robustly responds to the periodic driving subharmonically, with a period being the greatest common divisor of the original two periods. Existing theoretical analysis from many-body localization fails to understand the rigidity of such subspace-thermal time crystal phases. To resolve this, we develop a new theoretical framework from the perspective of the robust $2\pi/n$ quasi-energy gap. Its robustness is analytically proved, under a reasonable conjecture, by a new perturbation theory for unitary operators. The proof applies beyond the models considered here to other existing discrete time crystals realized by kicking disordered systems, thus offering a systematic way to construct new discrete time crystal models. We also introduce the notion of DTC-charges that allow us to probe the observables that spontaneously break the time-translation symmetry in both the regular discrete time crystals and subspace-thermal discrete time crystals. Moreover, our discrete time crystal models can be generalized to higher spin magnitudes or qudits, as well as higher spatial dimensions.

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