Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1710.00650 · Physics Letters B

Functional renormalization group and Kohn–Sham scheme in density functional theory

Haozhao Liang, Yifei Niu, Tetsuo Hatsuda

Published Feb 21, 2018• 32 citations
arXivHTMLPDF

Abstract

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn–Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

DOI
10.1016/j.physletb.2018.02.034

Related papers

Density Functional Theory with uncertainty quantification from Functional Renormalization Group in Kohn-Sham scheme

Haozhao Liang, Y. Niu, Tetsuo Hatsuda

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the $\varphi^4$ theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

•Sep 19, 2017•0 citations

Kohn–Sham equations with functionals from the strictly-correlated regime: investigation with a spectral renormalization method

Juri Grossi, Ziad H. Musslimani, Michael Seidl +1 more

We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory, with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential.

arXiv:2004.10436•Journal of Physics Condensed Matter•Aug 6, 2020•10 citations

Microscopic derivation of density functional theory for superfluid systems based on effective action formalism

Takeru Yokota, Haruki Kasuya, Kenichi Yoshida +1 more

Abstract A density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and non-local pairing densities and demonstrate that the Hohenberg–Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from $0$ to $1$, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn–Sham potential generalized to include the pairing potentials. The resultant Kohn–Sham potential has a nice feature in that it expresses the microscopic formulae of the external, Hartree, pairing and exchange–correlation terms separately. It is shown that our Kohn–Sham potential gives the ground-state energy of the Hartree–Fock–Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to improve the correlation part systematically.

arXiv:2008.05919•Progress of Theoretical and Experimental Physics•Dec 1, 2020•10 citations

A Rigorous Extension of the Kohn-Sham Equation for Strongly Correlated Electron Systems

Koichi Kusakabe

By introducing a set of auxiliary equations representing a many-body system, we have derived an extension of the Kohn-Sham scheme for the density functional theory. These equations consist of a Kohn-Sham-type equation determining single-particle orbitals and an eigen-value equation for an effective many-body problem. A variational method similar to the Kohn-Sham technique was utilized to derive effective interactions as well as effective potentials without artificial substitution of a Hubbard-type interaction and a mean-field correction in the energy functional. The second equation is described by an effective many-body Hamiltonian with both 2-body interactions and mean-field terms. Rigorous formulation of the extended Kohn-Sham equation is also given in accordance with the Hadjisavvas-Theophilou formulation. Our formulation can be interpreted as a way to define models of the strongly correlated electron systems, e.g. the Hubbard model

arXiv:cond-mat/0103094•Journal of the Physical Society of Japan•Jul 15, 2001•23 citations

Density-Functional Theory for Strongly Interacting Electrons

Paola Gori‐Giorgi, Michael Seidl, Giovanni Vignale

We present an alternative to the Kohn-Sham formulation of density-functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically expand the universal energy functional of the density in powers of a "coupling constant" that controls the magnitude of the kinetic energy. The problem of minimizing the energy is reduced to the solution of a strictly correlated electron problem in the presence of an effective potential, which in our theory plays the same role as the Kohn-Sham potential plays in the traditional formulation. We discuss several schemes for approximating the energy functional, and report preliminary results for low-density quantum dots.

arXiv:0908.0669•Physical Review Letters•Oct 12, 2009•106 citations

Functional methods for quantum thermodynamics

Sibo Wang, Samuel Degen, Haozhao Liang

The functional renormalization group provides a nonperturbative and systematically improvable route to constructing density functionals for quantum many-body systems from microscopic Hamiltonians. Here we advance this program by benchmarking functional-renormalization-group density functional theory (FRG-DFT) against the exact thermodynamics of the single-site Bose-Hubbard model. This model provides an ideal testing ground because it is analytically solvable, yet remains subtle in the imaginary-time coherent-state path integral, where a naive continuum treatment generates a spurious self-interaction. We show that a careful Hubbard-Stratonovich derivation identifies the self-interaction correction term that must be included in the FRG-DFT flow to recover the exact thermodynamics. We then systematically compare several closures of the resulting hierarchy of flow equations for the free energy, chemical potential, and connected density correlators over broad ranges of density, temperature, and interaction strength. The benchmark shows that the free energy is comparatively robust, whereas the chemical potential and fluctuation observables provide much sharper diagnostics of the hierarchy closure. A maximum-entropy closure gives the most accurate overall description and reproduces even the low-temperature oscillatory structure of the connected two-density correlator. These results identify two general requirements for functional approaches to quantum thermodynamics: the renormalization group flow equation must retain the equal-time contact subtraction to avoid spurious self-interactions, and any closure of the hierarchy must preserve the statistical consistency of density correlators. This work provides a controlled foundation for deriving ab initio density functionals for quantum many-body systems across condensed-matter, ultracold-atom, and nuclear physics, as well as quantum chemistry.

arXiv:2605.31112•May 29, 2026•0 citations
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn–Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4\varphi^4φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.
We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory, with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential.
Abstract A density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and non-local pairing densities and demonstrate that the Hohenberg–Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from 000 to 111, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn–Sham potential generalized to include the pairing potentials. The resultant Kohn–Sham potential has a nice feature in that it expresses the microscopic formulae of the external, Hartree, pairing and exchange–correlation terms separately. It is shown that our Kohn–Sham potential gives the ground-state energy of the Hartree–Fock–Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to improve the correlation part systematically.
By introducing a set of auxiliary equations representing a many-body system, we have derived an extension of the Kohn-Sham scheme for the density functional theory. These equations consist of a Kohn-Sham-type equation determining single-particle orbitals and an eigen-value equation for an effective many-body problem. A variational method similar to the Kohn-Sham technique was utilized to derive effective interactions as well as effective potentials without artificial substitution of a Hubbard-type interaction and a mean-field correction in the energy functional. The second equation is described by an effective many-body Hamiltonian with both 2-body interactions and mean-field terms. Rigorous formulation of the extended Kohn-Sham equation is also given in accordance with the Hadjisavvas-Theophilou formulation. Our formulation can be interpreted as a way to define models of the strongly correlated electron systems, e.g. the Hubbard model
We present an alternative to the Kohn-Sham formulation of density-functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically expand the universal energy functional of the density in powers of a "coupling constant" that controls the magnitude of the kinetic energy. The problem of minimizing the energy is reduced to the solution of a strictly correlated electron problem in the presence of an effective potential, which in our theory plays the same role as the Kohn-Sham potential plays in the traditional formulation. We discuss several schemes for approximating the energy functional, and report preliminary results for low-density quantum dots.
The functional renormalization group provides a nonperturbative and systematically improvable route to constructing density functionals for quantum many-body systems from microscopic Hamiltonians. Here we advance this program by benchmarking functional-renormalization-group density functional theory (FRG-DFT) against the exact thermodynamics of the single-site Bose-Hubbard model. This model provides an ideal testing ground because it is analytically solvable, yet remains subtle in the imaginary-time coherent-state path integral, where a naive continuum treatment generates a spurious self-interaction. We show that a careful Hubbard-Stratonovich derivation identifies the self-interaction correction term that must be included in the FRG-DFT flow to recover the exact thermodynamics. We then systematically compare several closures of the resulting hierarchy of flow equations for the free energy, chemical potential, and connected density correlators over broad ranges of density, temperature, and interaction strength. The benchmark shows that the free energy is comparatively robust, whereas the chemical potential and fluctuation observables provide much sharper diagnostics of the hierarchy closure. A maximum-entropy closure gives the most accurate overall description and reproduces even the low-temperature oscillatory structure of the connected two-density correlator. These results identify two general requirements for functional approaches to quantum thermodynamics: the renormalization group flow equation must retain the equal-time contact subtraction to avoid spurious self-interactions, and any closure of the hierarchy must preserve the statistical consistency of density correlators. This work provides a controlled foundation for deriving ab initio density functionals for quantum many-body systems across condensed-matter, ultracold-atom, and nuclear physics, as well as quantum chemistry.