  Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ)
theory were proposed [1]. They describe common properties of all known solved
systems with linearly time-dependent Hamiltonians. Here we show that ICs enable
efficient computer assisted search for new solvable MLZ models that span
complexity range from several interacting states to mesoscopic systems with
many-body dynamics and combinatorially large phase space. This diversity
suggests that nontrivial solvable MLZ models are numerous. In addition, we
refine the formulation of ICs and extend the class of solvable systems to
models with points of multiple diabatic level crossing.
