Quantum Mathematical Physics Seminar

I will review the basic workings of quantum integrability for spin chains of Heisenberg-type, such as the xxx chain. Such chains are short-range, with only nearest-neighbour interactions. There is a second recipe which produces long-range chains with interactions between all particle pairs, such as the Haldane-Shastry model, in which the integrable structure takes a different form. I will discuss this in details, and motivate why long-range models are interesting from both a physics and a mathematics perspective. Finally, I will present an overview of the chains which interpolate between the short- and long-range regimes and show all the hallmarks of quantum integrability. Working out the underlying theory should unify the two regimes, and allow us to construct integrable models with varying interaction strength.