Exploring variational methods with interpretable neural-networks and genetic algorithms

Neural-network based variational wave-functions have proven to be powerful tools to approximate ground states of complex many body Hamiltonians. They come, however, with several drawbacks: Their parameters are not physically motivated and thus an efficient parametrization is not guaranteed. In addition, the training of neural networks becomes challenging for systems where the ground state exhibits a non-trivial sign structure, e.g. frustrated models. We address these challenges by introducing a neural-network ansatz that allows for tunability with respect to the physics of the considered model. We illustrate its success on topological, long-range correlated and frustrated models. We further capitalize on the power of genetic algorithms in order to facilitate the training process and address non-differentiable variational optimization tasks. We introduce a set of methods for the variational exploration of excited states without symmetries.