Efficiency of the hidden fermion determinant states <i>Ansatz</i> in the light of different complexity measures

Finding reliable approximations to the quantum many-body problem is one of the central challenges of modern physics. Elemental to this endeavor is the development of advanced numerical techniques pushing the limits of what is tractable. One such recently proposed numerical technique are neural quantum states. This new type of wave-function-based utilizes the expressivity of neural networks to tackle fundamentally challenging problems, such as the Mott transition. In this paper, we aim to gauge the universalness of one representative of neural network , the hidden-fermion slater determinant approach. To this end, we study five different fermionic models each displaying volume law scaling of the entanglement entropy. For these, we correlate the effectiveness of the with different complexity measures. Each measure indicates a different complexity in the absence of which a conventional becomes efficient. We provide evidence that whenever one of the measures indicates proximity to a parameter region in which a conventional approach would work reliably, the neural network approach also works reliably and efficiently. This highlights the great potential of neural network approaches, but also the inherent challenges: finding suitable points in theory space around which to construct the in order to be able to efficiently treat models unsuitable for their current designs.