Symmetries and Many-Body Excitations with Neural-Network Quantum States.
- Choo K Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
- Carleo G Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA.
- Regnault N Laboratoire Pierre Aigrain, Ecole normale supérieure, PSL University, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, CNRS, 24 rue Lhomond, 75005 Paris France.
- Neupert T Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
- 2018-11-03
Published in:
- Physical review letters. - 2018
English
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.
- Language
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- English
- Open access status
- green
- Identifiers
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- DOI 10.1103/PhysRevLett.121.167204
- PMID 30387658
- Persistent URL
- https://folia.unifr.ch/global/documents/30072
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