Does causal dynamics imply local interactions?



University College London

June 1, 2022 3:15 PM


Quantum cellular automata (QCAs) are systems with causal dynamics in discrete spacetimes; one example being time-periodic quantum circuits. On one hand, we show that all quasi-free fermionic QCAs in one dimension can be generated by quasi-local Hamiltonians, that is, Hamiltonians with interactions which decay with the distance. On the other hand, we prove that some QCAs cannot be generated with quasi-local Hamiltonians. This also implies the existence of integrable system with no local, quasi-local nor low-weight constants of motion; a result that challenges the standard definition of integrability. Finally, we see that QCAs with disorder display a new form of many-body localisation.

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