TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.3.063
TI  - Hamiltonian reconstruction as metric for variational studies
PY  - 2022/09/23
UR  - https://www.scipost.org/SciPostPhys.13.3.063
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 3
SP  - 063
A1  - Zhang, Kevin
AU  - Lederer, Samuel
AU  - Choo, Kenny
AU  - Neupert, Titus
AU  - Carleo, Giuseppe
AU  - Kim, Eun-Ah
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.13.3.063,
	title={{Hamiltonian reconstruction as metric for variational studies}},
	author={Kevin Zhang and Samuel Lederer and Kenny Choo and Titus Neupert and Giuseppe Carleo and Eun-Ah Kim},
	journal={SciPost Phys.},
	volume={13},
	pages={063},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.3.063},
	url={https://scipost.org/10.21468/SciPostPhys.13.3.063},
}