Machine learning density functional theory for the Hubbard model
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2019Access:
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Nelson J, Tiwari R, Sanvito S, Machine learning density functional theory for the Hubbard model, Physical Review B, 99, 7, 2019Download Item:
PhysRevB.99.075132.pdf (PDF) 546.4Kb
Abstract:
The solution of complex many-body lattice models can often be found by defining an energy functional of the
relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation
is enough to describe the system’s total energy. Similarly to standard density functional theory, however, the
exact functional is unknown, and suitable approximations need to be formulated. By using a deep-learning neural
network trained on exact-diagonalization results, we demonstrate that one can construct an exact functional for
the Hubbard model. In particular, we show that the neural network returns a ground-state energy numerically
indistinguishable from that obtained by exact diagonalization and, most importantly, that the functional satisfies
the two Hohenberg-Kohn theorems: for a given ground-state density it yields the external potential, and it is fully
variational in the site occupation
URI:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.075132http://hdl.handle.net/2262/89982
Sponsor
Grant Number
European Research Council (ERC)
QUEST
Irish Research Council (IRC)
GOIPG/2016/1056
SFI/HEA Irish Centre for High-End Computing (ICHEC)
Author's Homepage:
http://people.tcd.ie/sanvitoshttp://people.tcd.ie/tiwarir
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PUBLISHED
Author: Sanvito, Stefano; Tiwari, Rajarshi
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Journal ArticleURI:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.075132http://hdl.handle.net/2262/89982
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Physical Review B99
7
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