Adiabatic Eigenstate Deformations and Weak Integrability Breaking of Heisenberg Chain

Explore the intricacies of spin-1/2 XXX chain dynamics in this comprehensive lecture on adiabatic eigenstate deformations and weak integrability breaking. Delve into the investigation of a Heisenberg chain weakly perturbed by an isotropic next-to-nearest neighbor exchange interaction. Examine the conjecture of an infinite tower of quasiconserved integrals of motion and learn how the norm of the adiabatic gauge potential (AGP) is used to test this hypothesis. Discover the unique behavior of the AGP norm in the perturbed XXX chain, which supports the model's quasi-integrability. Follow the proof of the conjecture and the construction of an infinite set of quasiconserved charges. Gain insights into how the perturbed XXX chain can be viewed as a truncation of an integrable long-range deformation of the Heisenberg spin chain, providing a deeper understanding of quantum spin systems and their behavior under perturbations.