Learning the Ghost Gutzwiller Embedding Variational Space
Oral-In-person
Abstract
Quantum Embedding (QE) methods often rely on an impurity model description, and efficient impurity solvers are fundamental components of QE calculations.
The recently developed Ghost-Gutzwiller Approximation (gGA) [1], in particular, relies on the knowledge of an eigenstate of the embedding Hamiltonian, which is usually chosen to be the ground state.
Although the impurity problem’s Fock space is exponentially large, the solutions of the gGA method lie in a low-dimensional latent space [2]. Learning this space enables significant computational speedups by projecting the impurity problem onto it.
Using an active learning approach based on Principal Component Analysis (PCA), we show[3] that learning the latent space of ground states around relevant Hamiltonians can accelerate gGA calculations by an order of magnitude. Moreover, this active learning procedure generalizes to other cases without retraining, as demonstrated here for a three-orbital Hubbard–Kanamori model.
These results prove that, within the gGA framework, a data-driven approach t the impurity solver step of the gGA cycle is possible and can substantially speed up calculations for strongly correlated multi-orbital problems, where gGA has already proven to be a reliable approach [4,5].
[1] N.Lanatà, T.H.Lee, Y.X. Yao, V.Dobrosavljević - Phys. Rev. B 96, 195126 (2017)
[2] M.S.Frank, D.G.Artiukhin, T.H.Lee, Y.X. Yao, K.Barros, O.Christiansen, N.Lanatà - Phys. Rev. Research 6, 01324 (2024)
[3] S.Giuli, H.Hasanat, B.Kloss, M.S.Frank, T.H. Lee, O.Gingras, Y.X.Yao, N.Lanatà - in preparation
[4] C.Mejuto-Zaera, M.Fabrizio - Phys. Rev. B 107, 235150 (2023)
[5] T.H. Lee, C.Melnick, R.Adler, N.Lanatà, G.Kotliar - Phys. Rev. B 108, 245147 (2023)
The recently developed Ghost-Gutzwiller Approximation (gGA) [1], in particular, relies on the knowledge of an eigenstate of the embedding Hamiltonian, which is usually chosen to be the ground state.
Although the impurity problem’s Fock space is exponentially large, the solutions of the gGA method lie in a low-dimensional latent space [2]. Learning this space enables significant computational speedups by projecting the impurity problem onto it.
Using an active learning approach based on Principal Component Analysis (PCA), we show[3] that learning the latent space of ground states around relevant Hamiltonians can accelerate gGA calculations by an order of magnitude. Moreover, this active learning procedure generalizes to other cases without retraining, as demonstrated here for a three-orbital Hubbard–Kanamori model.
These results prove that, within the gGA framework, a data-driven approach t the impurity solver step of the gGA cycle is possible and can substantially speed up calculations for strongly correlated multi-orbital problems, where gGA has already proven to be a reliable approach [4,5].
[1] N.Lanatà, T.H.Lee, Y.X. Yao, V.Dobrosavljević - Phys. Rev. B 96, 195126 (2017)
[2] M.S.Frank, D.G.Artiukhin, T.H.Lee, Y.X. Yao, K.Barros, O.Christiansen, N.Lanatà - Phys. Rev. Research 6, 01324 (2024)
[3] S.Giuli, H.Hasanat, B.Kloss, M.S.Frank, T.H. Lee, O.Gingras, Y.X.Yao, N.Lanatà - in preparation
[4] C.Mejuto-Zaera, M.Fabrizio - Phys. Rev. B 107, 235150 (2023)
[5] T.H. Lee, C.Melnick, R.Adler, N.Lanatà, G.Kotliar - Phys. Rev. B 108, 245147 (2023)
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Publication: S.Giuli, H.Hasanat, B.Kloss, M.S.Frank, T.H. Lee, O.Gingras, Y.X.Yao, N.Lanatà - "Accelerated Simulations of Strongly Correlated Matter by Machine-Learning the Ghost Gutzwiller Embedding Variational Space" - in preparation
Presenters
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Samuele Giuli
- Flatiron Institute