Does causal dynamics imply local interactions?
- URL: http://arxiv.org/abs/2006.10707v5
- Date: Mon, 27 Jun 2022 09:19:25 GMT
- Title: Does causal dynamics imply local interactions?
- Authors: Zolt\'an Zimbor\'as, Terry Farrelly, Szil\'ard Farkas, Lluis Masanes
- Abstract summary: We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA)
We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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