Does causal dynamics imply local interactions?

authored by

Zoltán Zimborás, Terry Farrelly, Szilárd Farkas, Lluis Masanes

Abstract

We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary. This can be written as the exponential of a Hamiltonian but in a highly non-unique way. We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers. On one hand, we present an example of QCA for which all generating Hamiltonians are fully non-local, in the sense that interactions do not decay with the distance. We expect this result to have relevant consequences for the classification of topological phases in Floquet systems, given that this relies on the effective Hamiltonian. On the other hand, we show that all one-dimensional quasi-free fermionic QCAs have quasi-local generating Hamiltonians, with interactions decaying exponentially in the massive case and algebraically in the critical case. We also prove that some integrable systems do not have local, quasi-local nor low-weight constants of motion; a result that challenges the standard definition of integrability.

Organisation(s)

Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)

External Organisation(s)

Hungarian Academy of Sciences
Budapest University of Technology and Economics
University of Queensland
University College London (UCL)

Type

Article

Journal

Quantum

Volume

6

No. of pages

9

ISSN

2521-327X

Publication date

2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics, Physics and Astronomy (miscellaneous)

Electronic version(s)

https://doi.org/10.48550/arXiv.2006.10707 (Access: Open)
https://doi.org/10.22331/Q-2022-06-29-748 (Access: Open)