Universität zu Köln

Zelle, Carl Philipp (2024). Universality in Time-Crystalline Matter. PhD thesis, Universität zu Köln.

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Abstract

In this dissertation we explore universal structures associated to time translation symmetry breaking in nonequlibrium O(N)-models. We extend the paradigmatic model A dynamics of a nonconserved order parameter (Hohenberg, Halpering, Rev.Mod.Phys. 1977) to include nonconservative forces driving it manifestly out of equilibrium. These lead to temporal instabilities towards phases that break time translation symmetry. The ensuing time crystalline order marks a nonthermal phase of matter beyond the Landau paradigm in equilibrium. We identify two different time-crystalline patterns, an oscillating phase and a rotating phase. Both of them are distinguished by the symmetry generators they break. By appropriate expansions of the underlying field theory, we analyse the critical phenomena associated to the instabilities towards time-crystalline order. This constitutes a generalization of the temporal instabilities defined in the classic work by Cross and Hohenberg (Cross, Hohenberg, Rev.Mod.Phys. 1993) to include noise, the crucial step to determine universal scaling behavior. At the finite frequency instability marking the transition between fully symmetric phase and a dynamical many-body limit cycle, we find that the critical degrees of freedom are described by an O(N)xSO(2) model. The additional SO(2) symmetry is an incarnation of time translations that are spontaneously broken along the transition. In a perturbative RG analysis in $d=4-\epsilon$ dimensions, we identify a novel, nonthermal universality class. Notably, even though the effective field theory could display an emergent thermal equilibrium, infinitesimal deviations from such an equilibrium suffice to push the system to the nonthermal fixed point on large scales. The transition between an ordered and the rotating phase is governed by a critical exceptional point, where a spectral nonanalyticity coincides with criticality. Such a point is impossible in equilibrium and leads to giant, superthermal fluctuations with nonanalytic dispersions. We show that these fluctuations can be controlled by a resummation of the perturbative series and establish that CEP fluctuations lead to a fluctuation induced first order transition. The breaking of time translation symmetry in the time crystalline phases leads to a soft Goldstone mode even in the absence of any internal symmetries. This mode realises the KPZ universality class leading to subexponential decaying correlations in low dimensions. The interplay with internal Goldstone modes in the O(N)xSO(2) model leads to additional novel regimes described by strongly interacting weak scaling fixed points in the one-loop flow equations. This paves the way to a potential extension of the KPZ phenomenology in higher symmetry groups. These phenomena can be realised in wide range of systems. We present a general approach to induce time-crystalline order by parametric pumps in systems that are subject to model A type dynamics in equilibrium. We also show that the presented universal scaling laws also apply in dynamic phases of nonreciprocally coupled matter. Surprisingly, this phenomenology can also be realised by arbitrarily weak drives. We demonstrate this for a light irradiated ferrimagnet.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Zelle, Carl Philipp czelle@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-749514
Date:	2024
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Nonequilibrium Phase Transitions UNSPECIFIED Time Crystals UNSPECIFIED Active Matter UNSPECIFIED
Date of oral exam:	6 December 2024
Referee:	Name Academic Title Diehl, Sebastian Prof. Dr. Krug, Joachim Prof. Dr. Hanai, Ryo Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/74951