Does causal dynamics imply local interactions?
Abstract
We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to timediscreteness this type of dynamics is not characterized by a Hamiltonian but by a onetimestep unitary. This can be written as the exponential of a Hamiltonian but in a highly nonunique 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 nonlocal, in the sense that interactions do not decay with the distance. On the other hand, we show that all onedimensional quasifree fermionic QCAs have quasilocal 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, quasilocal nor lowweight constants of motion; a result that challenges the standard classification of integrability.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.10707
 Bibcode:
 2020arXiv200610707Z
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 7+2 pages