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The concept of quantum integrability has been introduced recently for quantumsystems with explicitly time-dependent Hamiltonians. Within the multistateLandau-Zener (MLZ) theory, however, there has been a successful alternativeapproach to identify and solve complex time-dependent models. Here we compareboth methods by applying them to a new class of exactly solvable MLZ models.This class contains systems with an arbitrary number $N\ge 4$ of interactingstates and shows a quickly growing with $N$ number of exact adiabatic energycrossing points, which appear at different moments of time. At each $N$,transition probabilities in these systems can be found analytically and exactlybut complexity and variety of solutions in this class also grow with $N$quickly. We illustrate how common features of solvable MLZ systems appear fromquantum integrability and develop an approach to further classification ofsolvable MLZ problems.

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