Hamiltonian reconstruction as metric for variational studies

TL;DR

This paper introduces a Hamiltonian reconstruction method to evaluate the quality of neural-network variational wavefunctions in quantum many-body problems, revealing insights into their physical properties and limitations.

Contribution

It presents a novel multi-faceted approach using Hamiltonian reconstruction to assess neural-network based variational wavefunctions in quantum physics.

Findings

Reconstructed Hamiltonians are less frustrated and exhibit easy-axis anisotropy near high frustration points.

Reconstructed Hamiltonians suppress quantum fluctuations in the large J2 limit.

Wavefunction symmetry is critically important for accurate variational states.

Abstract

Variational approaches are among the most powerful modern techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in variational quantum eigensolvers. However, self-consistent evaluation of the quality of variational wavefunctions is a notoriously hard task. Using a recently developed Hamiltonian reconstruction method, we propose a multi-faceted approach to evaluating the quality of neural-network based wavefunctions. Specifically, we consider convolutional neural network (CNN) and restricted Boltzmann machine (RBM) states trained on a square lattice spin-1/2 $J_1$-$J_2$ Heisenberg model. We find that the reconstructed Hamiltonians are typically less frustrated, and have easy-axis anisotropy near the high frustration point. Furthermore, the reconstructed Hamiltonians suppress quantum fluctuations in the large $J_2$ limit. Our results highlight the critical importance of the wavefunction's symmetry. Moreover, the multi-faceted insight from the Hamiltonian reconstruction reveals that a variational wave function can fail to capture the true ground state through suppression of quantum fluctuations.