Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures

TL;DR

This paper evaluates the effectiveness of the hidden-fermion Slater determinant neural network Ansatz across various fermionic models, revealing its potential and limitations in relation to different complexity measures and traditional methods.

Contribution

It systematically assesses the universality and efficiency of the neural network Ansatz for fermionic models using multiple complexity measures, providing insights into its applicability and challenges.

Findings

Neural network Ansatz works reliably near parameters where conventional methods succeed.

Different complexity measures correlate with the effectiveness of the neural approach.

Identifies challenges in selecting suitable points in theory space for neural Ansatz construction.

Abstract

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 wavefunction based Ans\"atze 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 Ans\"atze, 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 Ansatz with different complexity measures. Each measure indicates a different complexity in the absence of which a conventional Ansatz becomes efficient. We provide evidence that whenever one of the measures indicates proximity to a parameter region in which a conventional approach would work reliable, the neural network approach also works reliable and efficient. This highlights the great potential, but also challenges for neural network approaches: Finding suitable points in theory space around which to construct the Ansatz in order to be able to efficiently treat models unsuitable for their current designs.