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Discrete time crystals beyond the MBL paradigm



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Discrete time crystals (DTCs) are systems that, subject to a periodic forcing, respond with a period larger than that of the drive. Breaking the discrete time-translational symmetry of the underlying equations, DTCs maintain an infinite autocorrelation time, avoid ergodicity, and realize a novel nonequilibrium phase of matter. In most previous proposals of DTCs, this peculiar behavior relied on the presence of (strong) disorder. Indeed, according to the celebrated mechanism of many-body localization (MBL), disorder can avert the otherwise generally expected 'heat death' to a featureless infinite temperature state in a driven system. And yet, it has recently been discovered that alternative mechanisms do exist through which thermalization can be avoided or significantly slowed down, such as confinement from long-range interactions, so-called quantum scars, or dynamical localization. This raises a number of natural questions: To what extent is MBL needed to observe nontrivial dynamics? What classifies a dynamics as nontrivial? What mechanisms can stabilize what phenomenologies of time crystallinity? Are DTCs possible in a classical setting and in which sense? In this dissertation, we address these questions proposing and investigating various remarkable notions of DTCs beyond the MBL-paradigm. Our journey across the zoology of time crystallinity embraces both the quantum and the classical realms, and discusses DTCs in their quasi, higher-order, fractional, and classical-stochastic flavours. All these exotic phenomena are encompassed by a unifying framework that we develop. Following this common thread, we justify and emphasise the key elements that, we think, should characterise DTCs, namely their many-body nature and the concept of universality in the nonequilibrium setting. Bringing together problems from different fields such as condensed matter physics, statistical physics, dynamical system theory, and epidemiology, we unveil striking ramifications of these remarkable dynamical phases of matter, advance our current understanding of many-body nonequilibrium phenomena, and pave the way towards new potential research avenues lying at the interface between multiple branches of science.





Nunnenkamp, Andreas
Lamacraft, Austen


Time crystals, Many-body systems, Periodically driven systems, Nonequilibrium phases of matter


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
Royal Society