FisMat2017 - Submission - View

Abstract's title: Floquet time-crystal in the Lipkin-Meshkov-Glick model
Submitting author: Angelo Russomanno
Affiliation: ICTP and Scuola Normale Superiore
Affiliation Address: ICTP: Strada Costiera 11, 34151, Trieste SNS: Piazza dei Cavalieri 1, 56126 Pisa
Country: Italy
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations: Fernando Iemini (ICTP Trieste), Marcello Dalmonte (ICTP Trieste), Rosario Fazio (ICTP Trieste and Scuola Normale Superiore, NEST & Istituto Nanoscienze Pisa)

In this talk I will discuss the existence of time-translation symmetry breaking in a kicked infinite-
range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquet
time-crystal is robust under perturbations of the kicking protocol, its existence being intimately
linked to the underlying Z2 symmetry breaking of the time-independent model. I will show that
the model being infinite-range and having an extensive amount of symmetry breaking eigenstates
is essential for having the time-crystal behaviour. In particular I will discuss the properties of the
Floquet spectrum, and show the existence of doublets of Floquet states which are respectively
even and odd superposition of symmetry breaking states and have quasi-energies differing of half
the driving frequencies, a key essence of Floquet time-crystals. Remarkably, the stability of the
time-crystal phase can be directly analysed in the limit of infinite size, discussing the properties
of the corresponding classical phase space.