Reduced Density Matrix Functional Theory for Bosons

Benavides-Riveros, Carlos L.; Wolff, Jakob; Marques, Miguel A. L.; Schilling, Christian

doi:10.1103/physrevlett.124.180603

Cited by 35 publications

(41 citation statements)

References 45 publications

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“…As an outlook, we think it will be important to incorporate and test our results for realistic 3D systems or include in the training data diffusive anion states in the sense of [41,42]. We also expect that our results can stimulate research on similar problems for ensemble DFT (understood as mixtures of ground and excites states), orbital free DFT or functional theories of reduced density matrices [57][58][59][60][61][62].…”

Section: Discussionmentioning

confidence: 90%

Machine learning the derivative discontinuity of density-functional theory

Gedeon

Schmidt

Hodgson

et al. 2021

Mach. Learn.: Sci. Technol.

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Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (a) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (b) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.

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Section: Discussionmentioning

confidence: 90%

Machine learning the derivative discontinuity of density-functional theory

Gedeon

Schmidt

Hodgson

et al. 2021

Mach. Learn.: Sci. Technol.

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“…Finally, since the maximum value of the functional F W [γ] is N (N − 1)/2 (see supplemental material of Ref. [21]) and α = N/2, we have that F ⊥ W [γ] − F W [γ] > 0, and therefore:…”

Section: Universal Functional For the Bose-hubbard Modelmentioning

confidence: 99%

“…The exact known results for M = 2 (8) are verified in our calculations. Furthermore, we observe the existence of the Bose-Einstein force [21,22,58], namely, the divergence of the gradient ∂ η F N,M (η) → (N − N BEC ) ζ , with ζ < 0, when approaching to the condensation point (i.e., η → 1). The prefactor of such a divergence is observed to be proportional to α(N − 1).…”

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confidence: 97%

“…They have also become an active research field in the con- * carlosbe@pks.mpg.de text of quantum simulations [14][15][16], and even quantum foundations [17][18][19][20]. Such need to describe quantum correlations of bosonic systems efficiently has motivated quite recently to put forward a novel physical theory for interacting bosonic systems [21,22]. Based on a generalization of the Hohenberg-Kohn theorem [23,24], this bosonic reduced density matrix functional theory (RDMFT) establishes the existence of a universal functional F W [γ] of the one-body reduced density matrix (1RDM): γ ≡ N Tr N −1 [Γ], obtained from the N -boson density operator Γ by integrating out all except one boson, and the two-particle interaction W .…”

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confidence: 99%

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Machine Learning Universal Bosonic Functionals

Schmidt,

Fadel,

Benavides-Riveros

2021

Preprint

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“…Local attractive interactions have been the subject of multiple theoretical studies by using a variety of methodologies [14][15][16][17][18][22][23][24][25][26][27][28][29][30]. In early works the formation and stability of charge-density waves (CDWs) and superconducting states has been quantified [14 and 15].…”

Section: Introductionmentioning

confidence: 99%

Density-matrix functional theory of the attractive Hubbard model: Statistical analogy of pairing correlations

Müller¹,

Pastor²

2021

Preprint

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The ground-state properties of the Hubbard model with attractive local pairing interactions are investigated in the framework of lattice density-functional theory. A remarkable correlation is revealed between the interaction-energy functional W [η] corresponding to the Bloch-state occupationnumber distribution η kσ and the entropy S[η] of a system of non-interacting fermions having the same η kσ . The relation between W [η] and S[η] is shown to be approximately linear for a wide range of ground-state representable occupation-number distributions η kσ . Taking advantage of this statistical analogy, a simple explicit ansatz for W [η] of the attractive Hubbard model is proposed, which can be applied to arbitrary periodic systems. The accuracy of this approximation is demonstrated by calculating the main ground-state properties of the model on several 1D and 2D bipartite and non-bipartite lattices and by comparing the results with exact diagonalizations.

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Reduced Density Matrix Functional Theory for Bosons

Cited by 35 publications

References 45 publications

Machine learning the derivative discontinuity of density-functional theory

Machine learning the derivative discontinuity of density-functional theory

Machine Learning Universal Bosonic Functionals

Density-matrix functional theory of the attractive Hubbard model: Statistical analogy of pairing correlations

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