Hamiltonian reconstruction as metric for variational studies
Kevin Zhang, Samuel Lederer, Kenny Choo, Titus Neupert, Giuseppe Carleo, Eun-Ah Kim
SciPost Phys. 13, 063 (2022) · published 23 September 2022
- doi: 10.21468/SciPostPhys.13.3.063
Variational approaches are among the most powerful 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 J1-J2 Heisenberg model. We find that the reconstructed Hamiltonians are typically less frustrated, and have easy-axis anisotropy near the high frustration point. In addition, the reconstructed Hamiltonians suppress quantum fluctuations in the large J2 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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Kevin Zhang,
- 1 Samuel Lederer,
- 2 Kenny Choo,
- 2 Titus Neupert,
- 3 Giuseppe Carleo,
- 1 Eun-Ah Kim
- 1 Cornell University [CU]
- 2 Universität Zürich / University of Zurich [UZH]
- 3 École Polytechnique Fédérale de Lausanne [EPFL]