Quantum Singwi-Tosi-Land-Sjölander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results

Kosugi, Taichi; Matsushita, Yu-ichiro

doi:10.1063/1.4994720

Cited by 3 publications

(7 citation statements)

References 39 publications

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Section: B Two-electron Systemmentioning

confidence: 99%

“…The exact KS potential for our interacting two-electron system is calculated from eqs. (7) and (64) as [22]…”

Section: Kohn-sham Green's Functionmentioning

confidence: 99%

“…This model has been studied intensively. [19][20][21][22] The variable transformation for the center-of-mass coordinate x + ≡ (x 1 + x 2 )/2 and the scaled relative coordinate x − ≡ (x 1 − x 2 )/ √ 2 decouples the interacting Hamiltonian into two Hamiltonians for independent harmonic oscillators as H (2) = H HO (x + ; M 2 , ω 0 ) + H HO (x − ; m e , ω r ), where M 2 ≡ 2m e and ω r ≡ √ 1 − 2Λω 0 ≡ λ 2 ω 0 . The solution for the center-of-mass motion is…”

Section: B Two-electron Systemmentioning

confidence: 99%

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One-particle Green’s function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn–Sham system

Kosugi¹,

Matsushita²

2018

J. Phys.: Condens. Matter

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For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schrödinger equation analytically to obtain the exact solutions, from which we construct explicitly the simultaneous eigenstates of the energy and total spin for the first time. The solutions for the three-electron system allow us to derive analytic expressions for the exact one-particle Green's function (GF) for the corresponding two-electron system. We calculate the GF in frequency domain to examine systematically its behavior depending on the electronic interactions. We also compare the pole structure of non-interacting GF using the exact Kohn-Sham (KS) potential with that of the exact GF to find that the discrepancy of the energy gap between the KS system and the original system is larger for a stronger interaction. We perform numerical examination on the behavior of GFs in real space to demonstrate that the exact and KS GFs can have shapes quite different from each other. Our simple model will help to understand generic characteristics of interacting GFs.

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Section: B Two-electron Systemmentioning

confidence: 99%

“…The exact KS potential for our interacting two-electron system is calculated from eqs. (7) and (64) as [22]…”

Section: Kohn-sham Green's Functionmentioning

confidence: 99%

Section: B Two-electron Systemmentioning

confidence: 99%

See 1 more Smart Citation

One-particle Green’s function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn–Sham system

Kosugi¹,

Matsushita²

2018

J. Phys.: Condens. Matter

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“…This method attempts to tackle in an approximate manner both the exchange and electronic correlations through a local-field correction. As such, this scheme is often surprisingly accurate in the description of the full electronic density response and is commonly used to investigate quasi-one-dimensional [39], inhomogeneous [40][41][42] and warm dense electron liquids [43][44][45]. It has also inspired the development of new functional methods that explicitly retain the dynamical and non-local nature of electronic correlations, while properly accounting for the exchange contribution [46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Homogeneous electron liquid in arbitrary dimensions beyond the random phase approximation

Duc Pham,

Sattler,

Marques

et al. 2023

New J. Phys.

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The homogeneous electron liquid is a cornerstone in quantum physics and chemistry. It is an archetypal system in the regime of slowly varying densities in which the exchange-correlation energy can be estimated with many methods. For high densities, the behavior of the ground-state energy is well-known for 1, 2, and 3 dimensions. Here, we extend this model to arbitrary integer dimensions and compute its correlation energy beyond the random phase approximation (RPA). We employ the approach developed by Singwi, Tosi, Land, and Sjölander (STLS), whose description of the electronic density response for 2D and 3D for metallic densities is known to be comparable to Quantum Monte-Carlo. For higher dimensions, we compare the results obtained for the correlation energy with the values previously obtained using RPA. We find that in agreement with what is known for 2 and 3 dimensions, the RPA tends to over-correlate the liquid also at higher dimensions. We furthermore provide new analytical formulae for the unconventional-dimensional case both for the real and imaginary parts of the Lindhard polarizability and for the local field correction of the STLS theory and illustrate the importance of the plasmon contribution at those high dimensions.

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“…The charge and spin response functions, formulated in the linear-response theory [23,24], describe the leading contributions to the electric and magnetic excitations when perturbation fields are applied to a target system. Since the response functions are the fundamental building blocks in constructing the elaborated methods for correlated electrons such as GW theory [23,25], the accurate calculation of them is needed.…”

Section: Introductionmentioning

confidence: 99%

Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

Kosugi

Matsushita

2020

Phys. Rev. Research

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We propose a scheme for the construction of linear-response functions of an interacting electronic system via quantum phase estimation and statistical sampling on a quantum computer. By using the unitary decomposition of electronic operators for avoiding the difficulty due to their nonunitarity, we provide the circuits equipped with ancillae for probabilistic preparation of qubit states on which the necessary nonunitary operators have acted. We perform simulations of such construction of the charge and spin response functions and photoabsorption cross sections for C 2 and N 2 molecules by comparing with the results from full configuration-interaction calculations. It is found that the accurate detection of subtle structures coming from the weak poles in the response functions requires a large number of measurements.

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Quantum Singwi-Tosi-Land-Sjölander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results

Cited by 3 publications

References 39 publications

One-particle Green’s function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn–Sham system

One-particle Green’s function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn–Sham system

Homogeneous electron liquid in arbitrary dimensions beyond the random phase approximation

Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

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