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Symmetries and Many-Body Excitations with Neural-Network Quantum States
Open accessAbstract
Artificial neural networks have been recently introduced as a general ansatz to represent many-body wave functions. In conjunction with variational Monte Carlo calculations, this ansatz has been applied to find Hamiltonian ground states and their energies. Here, we provide extensions of this method to study excited states, a central task in several many-body quantum calculations. First, we give a prescription that allows us to target eigenstates of a (nonlocal) symmetry of the Hamiltonian. Second, we give an algorithm to compute low-lying excited states without symmetries. We demonstrate our approach with both restricted Boltzmann machines and feed-forward neural networks. Results are shown for the one-dimensional spin-1/2 Heisenberg model, and for the one-dimensional Bose-Hubbard model. When comparing to exact results, we obtain good agreement for a large range of excited-states energies. Interestingly, we find that deep networks typically outperform shallow architectures for high-energy states.
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Self-citationMachine learning phases of matter
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Machine Learning for Electronically Excited States of Molecules
Westermayr, J., & Marquetand, P. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.0c00749 · Cited by 398
Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems
Sharir, O., Levine, Y., Wies, N., Carleo, G., & Shashua, A. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.020503 · Cited by 256
Self-citationNetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
Vicentini, F., Hofmann, D., Szabó, A., Wu, D., Roth, C., Giuliani, C., Pescia, G., Nys, J., Vargas-Calderón, V., Astrakhantsev, N., et al. (2022) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.7 · Cited by 135
Self-citationQuantum phase transition dynamics in the two-dimensional transverse-field Ising model
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Metadata
- Authors
- Choo, K., Carleo, G., Regnault, N., & Neupert, T.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2018-10-19
- Volume
- 121
- Issue
- 16
- Pages
- 167204-167204
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2845055700
- Cited by
- 245
- References
- 6
- FWCI
- 11.10
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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