After an introduction to the relevant topics, we present a continuous-time crystal based on a quantum black-hole laser, where the genuinely spontaneous character of the symmetry breaking stems from the self-amplification of spontaneous Hawking radiation [1]. The resulting Hawking time crystal (HTC) is characterized by the periodic dependence of the out-of-time density-density correlation function, while equal-time observables are time-independent because they embody averages over different realizations with a random oscillation phase. The HTC can be regarded as a nonlinear periodic analogue of the Andreev-Hawking effect, exhibiting anticorrelation bands resulting from the spontaneous, quantum emission of pairs of dispersive waves and solitons into the upstream and downstream regions. Remarkably, the time-crystal formation is understood in terms of two time operators: one associated to the initial black-hole laser and another associated to the final spontaneous Floquet state [2,3]. Time permitting, we will briefly discuss some recent work on the realization of Sachdev-Ye-Kitaev (SYK) physics from the shaking of the Hubbard model [4].
[1] J. R. Muñoz de Nova, F. Sols. Time Crystal from Self-Amplification of Spontaneous Analog Hawking Radiation. Phys. Rev. Lett. 136, 170402 (2026).
[2] J. R. M. de Nova, F. Sols. Continuous-time crystal from a spontaneous many-body Floquet state. Phys. Rev. A 105, 043302 (2022).
[3] J. R. Muñoz de Nova, F. Sols, Simultaneous symmetry breaking in spontaneous Floquet states: temporal Floquet-Nambu-Goldstone modes, Floquet thermodynamics, and the time operator. Quantum 9, 1850 (2025).
[4] C. Creffield, F. Sols, M. Schirò, N. Goldman. Sachdev-Ye-Kitaev Physics from the Hubbard Model: A Floquet-Engineering Approach. Phys. Rev. Lett. 137, 046302 (2026).
Work supported by Spain’s MICIU/AEI through Proyectos de Generación de Conocimiento under Grant No. PID2022-139288NB-I00.
Fernando Sols, Professor, Complutense University, Madrid
Host: William Halperin
Joan West
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