A large class of solvable multistate Landau-Zener models and quantum integrability

We identify a new class of exactly solvable multistate Landau-Zener (MLZ) models. Such models can have an arbitrary number N of interacting states and quickly growing with N numbers of exact adiabatic energy crossing points, which appear at different values of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. By exploring several low-dimensional sectors, we find features that shed light on the common properties of these solutions and, generally, on quantum integrability. We also show that the previously known bowtie model can be entirely derived as a special limit of our solvable class.