Affiliation:
1. Eötvös Loránd University
Abstract
We consider one dimensional block cellular automata, where the local
update rules are given by Yang-Baxter maps, which are set theoretical
solutions of the Yang-Baxter equations. We show that such systems are
superintegrable: they possess an exponentially large set of conserved
local charges, such that the charge densities propagate ballistically on
the chain. For these quantities we observe a complete absence of
"operator spreading". In addition, the models can also have other local charges which are conserved only additively. We discuss concrete models up to local dimensions N \le 4N≤4, and show that they give rise to rich physical behaviour, including non-trivial scattering of particles and the coexistence of ballistic and diffusive transport. We find that the local update rules are classical versions of the "dual
unitary gates" if the Yang-Baxter maps are non-degenerate. We discuss
consequences of dual unitarity, and we also discuss a family of dual
unitary gates obtained by a non-integrable quantum mechanical
deformation of the Yang-Baxter maps.
Subject
General Physics and Astronomy
Cited by
14 articles.
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