Speaker
Description
We explore the integrability of the 1+1-dimensional massless Thirring Quantum Cellular Automaton, which describes the discrete-time evolution of fermionic modes on a lattice with local, number-preserving interactions. The interaction serves as a discrete-time analogue of those found in integrable Hamiltonian systems such as the Thirring and Hubbard models. Using the coordinate Bethe ansatz, we analyse the spectrum of the unitary operator defining the QCA dynamics, constructing translationally invariant eigenstates as superpositions of plane waves related by permutations of particle spins and momenta. The discrete-time structure leads to distinctive features absent in continuous-time systems, in particular constraints arising from the periodicity of the quasi-energy spectrum, which induce degeneracies. We derive consistency relations among the amplitudes and show that they can be encoded in a two-body scattering matrix satisfying the Yang–Baxter equation. In the massless case, however, the dynamics renders this structure effectively trivial, reflecting strong kinematic constraints while preserving the characteristic form of the scattering matrix. These results provide the foundation for ongoing work on the massive case, where the insights gained here guide the construction of the Bethe ansatz and the treatment of the distinctive features of the QCA dynamics.