Adiabatic deformations and weak integrability breaking in the Heisenberg model

We cosider the isotropic Heisenberg model of 1/2 spins excited by next-to-nearest neighbor interaction. Earlier it was suggested that in this model, there is an infinite set of local quasi-charges — such quantities that "almost" commute with the Hamiltonian. In this talk, I will discuss the relationship between such a quasi-integrable structure and adiabatic deformations. It turns out that the norm of the generator of adiabatic deformations allows us to distinguish quasi-integrable excitations from excitations that violate the integrability completely. Moreover, with the help of such a generator in the model under consideration, we manage to construct all quasi-charges explicitly.
The report is based on the work arxiv.org/abs/2303.00729