One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

Giesbertz, Klaas J. H.; Ruggenthaler, Michael

doi:10.1016/j.physrep.2019.01.010

Cited by 35 publications

(66 citation statements)

References 134 publications

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“…One is to include temperature and possibly an indefinite number of particles, which introduces off-diagonals that depend on the temperature and the hopping, that is, the nonlocal potential. 19 We note that for the homogeneous two-site case, this can still be solved analytically and verified explicitly. The other possibility is to make the system degenerate such that we can reproduce any density matrix.…”

Section: Formulation Of the Lattice Problemmentioning

confidence: 85%

“…For 1RDM theory, it is helpful to consider the many-body problem at finite temperature and indefinite numbers of particles. 17 − 19 In this case, the representability conditions in terms of an ensemble of wave functions are known and easy to implement, and one can even find a noninteracting auxiliary system that generates the same 1RDM. Another possibility is to construct approximate natural orbitals, which are eigenfunctions of single-particle Hamiltonians with a local effective-potential.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic-Energy Density-Functional Theory on a Lattice

Θεοφίλου

Buchholz

Eich

et al. 2018

J. Chem. Theory Comput.

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We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn–Sham (keKS) scheme on a lattice and show that, by including more observables explicitly in a density-functional approach, already simple approximation strategies lead to very accurate results. Here, we promote the kinetic-energy density to a fundamental variable alongside the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. On the basis of this mapping, we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, which force the keKS system to generate the same kinetic-energy density and density as the fully interacting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density, that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn–Sham (KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems and comparing the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange (for the effective potential) and a uniform (for the effective hopping) approximation for the keKS and the exact-exchange approximation for the KS system, respectively.

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Section: Formulation Of the Lattice Problemmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Kinetic-Energy Density-Functional Theory on a Lattice

Θεοφίλου

Buchholz

Eich

et al. 2018

J. Chem. Theory Comput.

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“…This means the usual presentations of DFT already assume some form of regularization of the functionals. Other special forms of DFT like with internal magnetic fields [20] or finite temperatures [21,22] automatically include regularization effects.…”

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confidence: 99%

“…It also holds for CDFT on a finite lattice, since the current density is bounded by the hopping parameter [29,Eq. (25)], and for one-body reduced density matrix functional theory (RDMFT) in finite basis sets, since the off-diagonal elements of the reduced density matrix are bounded by the diagonal ones that give the usual density [22,Eq. (3.49)].…”

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confidence: 99%

Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions

et al. 2019

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The exact Kohn-Sham iteration of generalized density-functional theory in finite dimensions with a Moreau-Yosida regularized universal Lieb functional and an adaptive damping step is shown to converge to the correct ground-state density.The Kohn-Sham (KS) scheme [1] of ground-state density-functional theory (DFT) is the cornerstone of electronic structure calculations in quantum chemistry and solid-state physics [2]. It maps a complicated system of interacting electrons onto an auxiliary, non-interacting KS system. This yields a set of coupled one-particle equations that need to be solved self-consistently. Since a direct solution is unfeasible, practical approaches are variations of self-consistent field methods taking the form of fixed-point iterations or energy minimization algorithms [3][4][5][6][7][8]. To date, no method has been rigorously shown to converge to the correct ground-state density. Convergence results for approximate schemes are available for auxiliary assumptions [9], and reliably achieving convergence in systems with small band gaps or for transition metals remains a hard practical challenge [10]. Approximation techniques face the problem of an exponential growth of local minima with increasing number of particles [11]. Such local minima appear as 'false' solutions in the energy landscape and distract from the global, absolute minimum [12]. Hence, a method with mathematically guaranteed convergence to the correct minimizer is of central importance and has been listed as one of twelve outstanding problems in DFT [13].

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“…With ǫ = α/2, we have G = α∆ α 2 ∆ − c α/2 , and thus α 2 (−∆) c α/2 , which implies α = 0 and G = 0. We refer to [21] for a review about Matrix DFT at positive temperature. |s 1 , .…”

Section: 2mentioning

confidence: 99%

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

Garrigue

2019

J Stat Phys

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We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any ground state contain the information of the interactions and of the external potentials. Then, in the presence of the Zeeman interaction, a strong constraint on external fields is derived for systems having the same ground state densities and magnetizations. Next, we prove that the density and the entropy of a ground state contain the information of both the imposed external potential and temperature. Eventually, we conclude that at positive temperature, Hohenberg-Kohn theorems generically hold.

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One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

Cited by 35 publications

References 134 publications

Kinetic-Energy Density-Functional Theory on a Lattice

Kinetic-Energy Density-Functional Theory on a Lattice

Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

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