TY - JOUR

T1 - Does causal dynamics imply local interactions?

AU - Zimborás, Zoltán

AU - Farrelly, Terry

AU - Farkas, Szilárd

AU - Masanes, Lluis

N1 - Funding Information: The authors would like to thank Tobias J. Osborne for useful discussions. LM acknowledges financial support by the UK’s Engineering and Physical Sciences Research Council (grant number EP/R012393/1). TF was supported by the ERC grants QFTCMPS and SIQS, the cluster of excellence EXC201 Quantum Engineering and Space-Time Research, the DFG through SFB 1227 (DQ-mat), and the Australian Research Council Centres of Excellence for Engineered Quantum Systems (EQUS, CE170100009). ZZ acknowledges support from the János Bolyai Research Scholarship, the UKNP Bolyai+ Grant, and the NKFIH Grants No. K124152, K124176 KH129601, K120569, and from the Hungarian Quantum Technology National Excellence Program, Project No. 2017-1.2.1-NKP-2017-00001.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85134621290&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2006.10707

DO - 10.48550/arXiv.2006.10707

M3 - Article

AN - SCOPUS:85134621290

VL - 6

JO - Quantum

JF - Quantum

SN - 2521-327X

ER -