  Variational methods have proven to be excellent tools to approximate ground
states of complex many body Hamiltonians. Generic tools like neural networks
are extremely powerful, but their parameters are not necessarily physically
motivated. Thus, an efficient parametrization of the wave-function can become
challenging. In this letter we introduce a neural-network based variational
ansatz that retains the flexibility of these generic methods while allowing for
a tunability with respect to the relevant correlations governing the physics of
the system. We illustrate the success of this approach on topological,
long-range correlated and frustrated models. Additionally, we introduce
compatible variational optimization methods for exploration of low-lying
excited states without symmetries that preserve the interpretability of the
ansatz.
