Symmetries and conserved quantities of boundary time crystals in generalized spin models

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  • Giulia Piccitto
  • Matteo Wauters
  • Franco Nori
  • Nathan Shammah

We investigate how symmetries and conserved quantities relate to the occurrence of the boundary time crystal (BTC) phase in a generalized spin model with Lindblad dissipation. BTCs are a nonequilibrium phase of matter in which the system, coupled to an external environment, breaks the continuous time translational invariance. We perform a detailed mean-field study aided by a finite-size analysis of the quantum model of a p,q-spin-interaction system, a generalized p-spin-interaction system, which can be implemented in fully connected spin-1/2 ensembles. We find the following conditions for the observation of the BTC phase. First, the BTC appears when the discrete symmetry held by the Hamiltonian, Z2 in the considered models, is explicitly broken by the Lindblad jump operators. Second, the system must be coupled uniformly to the same bath in order to preserve the total angular momentum during the time evolution. If these conditions are not satisfied, any oscillatory behavior appears only as a transient in the dynamics and a time-independent stationary state is eventually reached. Our results suggest that these two elements may be general requirements for the observation of a stable BTC phase relating symmetries and conserved quantities in arbitrary spin models.

OriginalsprogEngelsk
Artikelnummer014307
TidsskriftPhysical Review B
Vol/bind104
Udgave nummer1
Antal sider17
ISSN2469-9950
DOI
StatusUdgivet - 2021

Bibliografisk note

Funding Information:
The authors acknowledge useful discussions with M. Burrello, M. Dalmonte, R. Fazio, F. Minganti, D. Rossini, G.E. Santoro, A. Silva, and F.M. Surace. G.P. thanks Giovanni Piccitto for useful comments. F.N. is supported in part by Nippon Telegraph and Telephone Corporation (NTT) Research, the Japan Science and Technology Agency (JST) [via the Quantum Leap Flagship Program (Q-LEAP), the Moonshot R&D Grant Number JPMJMS2061, and the Centers of Research Excellence in Science and Technology (CREST) Grant No. JPMJCR1676], the Japan Society for the Promotion of Science (JSPS) [via the Grants-in-Aid for Scientific Research (KAKENHI) Grant No. JP20H00134 and the JSPS-RFBR Grant No. JPJSBP120194828], the Army Research Office (ARO) (Grant No. W911NF-18-1-0358), the Asian Office of Aerospace Research and Development (AOARD) (via Grant No. FA2386-20-1-4069), and the Foundational Questions Institute Fund (FQXi) via Grant No. FQXi-IAF19-06. M.W. is supported by the Villum Foundation (Research Grant No. 25310). This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 847523 “INTERACTIONS.”

Publisher Copyright:
© 2021 American Physical Society.

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