Machine learning density functional theory for the Hubbard model Article Swipe
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· 2019
· Open Access
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· DOI: https://doi.org/10.1103/physrevb.99.075132
· OA: W2899081963
The solution of complex many-body lattice models can often be found by\ndefining an energy functional of the relevant density of the problem. For\ninstance, in the case of the Hubbard model the spin-resolved site occupation is\nenough to describe the system total energy. Similarly to standard density\nfunctional theory, however, the exact functional is unknown and suitable\napproximations need to be formulated. By using a deep-learning neural network\ntrained on exact-diagonalization results we demonstrate that one can construct\nan exact functional for the Hubbard model. In particular, we show that the\nneural network returns a ground-state energy numerically indistinguishable from\nthat obtained by exact diagonalization and, most importantly, that the\nfunctional satisfies the two Hohenberg-Kohn theorems: for a given ground-state\ndensity it yields the external potential and it is fully variational in the\nsite occupation.\n
