Subspace-thermal discrete time crystals from phase transitions between different n-tuple discrete time crystals
Abstract: A time crystal is a phase of matter that spontaneously breaks time translation symmetry. As it cannot appear in equilibrium and continuous time setting, most proposals of time crystals employ periodic i.e., Floquet driving and the response of the system breaks discrete time translation to, e.g., a period twice the driving. Here, 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 sub-harmonically, 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 2π/n quasi-energy gap. Its robustness is analytically proved, under a reasonable conjecture, by a new unitary perturbation theory. The proof applies beyond the models considered here to many other existing discrete time crystals realized by kicking disordered systems. It offers a systematic way to construct other 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 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.
This is based on work with my student Hongye Yu, arXiv:2409.02848.
Bio: Tzu-Chieh Wei obtained his PhD in Physics from the University of Illinois in 2004 and is currently a professor at the C. N. Yang Institute for Theoretical Physics at Stony Brook University. He works at the interdisciplinary quantum information science and has contributed to the development of the geometric measure of entanglement, quantum computational universality of two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) states, the existence of a nonzero spectral gap in AKLT models, the use of symmetry-protected topological states for measurement-based quantum computation, QMA-hardness complexity for bosonic problems, and applications of tensor-network methods in quantum many-body systems. He was also involved with several milestone experiments in quantum information processing. His recent interest includes error mitigation for near-term quantum processors and their benchmarking, quantum algorithms, and quantum simulations, as well as quantum many-body entanglement. He has spearheaded the effort that led to the creation of a quantum master’s program at Stony Brook University and has been collaborating with colleagues in quantum education for high school students and teachers.
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