The Thirring quantum cellular automaton

TL;DR

This paper analytically diagonalizes a discrete-time interacting fermionic cellular automaton, revealing unique scattering processes and bound states, including in the free case, differing from traditional Hamiltonian models.

Contribution

It provides an exact solution for a fermionic cellular automaton, highlighting novel features like bound states at all momenta and in the absence of coupling.

Findings

Wider variety of scattering processes observed

Bound states exist for all total momenta

Bound states also present in the free case

Abstract

We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in the two-particle sector. Important features of the solutions sensibly differ from those of analogous Hamiltonian models. In particular, we found a wider variety of scattering processes, we have bound states for every value of the total momentum, and there exist bound states also in the free case, where the coupling constant is null.