Hamiltonian reconstruction as metric for a variational study of the spin-1/2 J₁-J₂ Heisenberg model

Evaluating the quality of variational wavefunctions is a hard task due to the large dimensionality of Hilbert space. At the same time, modern methods such as artificial neural networks or variational quantum eigensolvers need accurate evaluation of wavefunctions to facilitate effective development. We propose using a recently developed Hamiltonian reconstruction method for a multi-faceted approach to evaluating wavefunctions. Starting from convolutional neural network and restricted Boltzmann machine ansatze trained on a square lattice spin-1/2 J₁-J₂ Heisenberg model, we compare reconstructed Hamiltonians to the original Hamiltonian to evaluate various aspects of the wavefunction. The reconstructed Hamiltonians are systematically 1) less frustrated, and 2) have easy-axis anisotropy near the high frustration point. Also, in the large J₂ limit, further-range interactions are induced in the reconstructions. This highlights the importance of implementing symmetries explicitly in neural network ansatze.