Genetic-tunneling driven energy optimizer for spin systems

A long-standing and difficult problem in, e.g., condensed matter physics is how to find the ground state of a complex many-body system where the potential energy surface has a large number of local minima. Spin systems containing complex and/or topological textures, for example spin spirals or magnetic skyrmions, are prime examples of such systems. We propose here a genetic-tunneling-driven variance-controlled optimization approach, and apply it to two-dimensional magnetic skyrmionic systems. The approach combines a local energy-minimizer backend and a metaheuristic global search frontend. The algorithm is naturally concurrent, resulting in short user execution time. We find that the method performs significantly better than simulated annealing (SA). Specifically, we demonstrate that for the Pd/Fe/Ir(111) system, our method correctly and efficiently identifies the experimentally observed spin spiral, skyrmion lattice and ferromagnetic ground states as a function of external magnetic field. To our knowledge, no other optimization method has until now succeeded in doing this. We envision that our findings will pave the way for evolutionary computing in mapping out phase diagrams for spin systems in general.