Speaker
Rustem Sharipov
(University of Ljubljana)
Description
The reversible cellular automaton Rule 54 (RCA 54) exhibits striking signatures of integrability, including stable solitons and ballistic transport. Nevertheless, a systematic structural formulation of its integrability has remained elusive.
In this talk, I discuss a new perspective on integrability in classical RCA 54. I introduce a mechanism of "integrability by projection", whereby interacting solitonic dynamics with nontrivial phase shifts emerge from a projection of SWAP dynamics. From the quantum perspective, using recent remarkable work by Paletta and Prosen (arXiv:2603.25424), I will show that quantum Rule 54 is a limit of a integrable trotterization of the bond-transformed Heisenberg spin chain.
Author
Rustem Sharipov
(University of Ljubljana)
Co-authors
Chiara Paletta
(University of Ljubljana)
Tomaž Prosen
(University of Ljubljana)