Prethermalization without Temperature

• Published in: Physical review. X Vol. 10; no. 2; p. 021046
• Main Authors: Luitz, David J., Moessner, Roderich, Sondhi, S. L., Khemani, Vedika
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 01.05.2020
• Subjects: Autocorrelation functions; Clean energy; Crystal structure; Crystallinity; Crystals; Energy absorption; Experiments; NMR; Nuclear magnetic resonance; Optimization; Signatures; Thermalization (energy absorption)
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.10.021046

While a clean, driven system generically absorbs energy until it reaches “infinite temperature,” it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for nontrivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localized cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al. [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.