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

Physical review. B, Condensed matter

Dynamic and static correlation functions in the inhomogeneous-Hartree-Fock-state approach with random-phase-approximation fluctuations

J. Lorenzana, Marcelo D. Grynberg, Lu Yu, Kenji Yonemitsu, A. R. Bishop

Published May 15, 1993• 8 citations
Publisher

Abstract

The ground-state energy and static and dynamic correlation functions are investigated in the inhomogeneous-Hartree-Fock (IHF) plus random-phase-approximation (RPA) approach applied to a one-dimensional spinless-fermion model showing self-trapped doping states at the mean-field level. Results are compared with those obtained using homogeneous HF and exact diagonalization. RPA fluctuations added to the generally inhomogeneous-HF ground state allow the computation of dynamical correlation functions that compare well with exact diagonalization results. The RPA correction to the ground-state energy agrees well with the exact results at strong- and weak-coupling limits. We also compare it with a related quasiboson approach. The instability towards self-trapped behavior is signaled by a RPA mode with frequency approaching zero.

DOI
10.1103/physrevb.47.13156

Related papers

Random phase approximation vs exact shell-model correlation energies

Ionel Stetcu, Calvin W. Johnson

The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full $0\ensuremath{\Elzxh}\ensuremath{\omega}$ shell-model spaces we calculate the Hartree-Fock $(\mathrm{HF})+\mathrm{RPA}$ binding energy, and compare it to exact diagonalization. We find that often, but not always, the $\mathrm{HF}+\mathrm{RPA}$ gives a good approximation to the ``exact'' ground state energy. In those cases where the RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wave function. This weakens the reliability of the RPA for computing binding energies.

arXiv:nucl-th/0205029•Physical Review C•Sep 3, 2002•37 citations

Inhomogeneous Gutzwiller approximation with random phase fluctuations for the Hubbard model

G. Seibold, Federico Becca, J. Lorenzana

We present a detailed study of the time-dependent Gutzwiller approximation for the Hubbard model. The formalism, labeled GA+RPA, allows us to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). No restrictions are imposed on the charge and spin configurations which makes the method suitable for the calculation of linear excitations around symmetry-broken solutions. Well-behaved sum rules are obeyed as in the Hartree-Fock (HF) plus RPA approach. Analytical results for a two-site model and numerical results for charge-charge and current-current dynamical correlation functions in one and two dimensions are compared with exact and HF+RPA results, supporting the much better performance of GA+RPA with respect to conventional HF+RPA theory.

arXiv:cond-mat/0209351•Physical review. B, Condensed matter•Feb 26, 2003•32 citations

Time-Dependent Gutzwiller Approximation for the Hubbard Model

G. Seibold, J. Lorenzana

We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard model analogous to the time-dependent Hartree-Fock (HF) method. This new formalism incorporates ground state correlations of the random phase approximation (RPA) type beyond the GA. Static quantities like ground state energy and double occupancy are in excellent agreement with exact results in one dimension up to moderate coupling and in two dimensions for all couplings. We find a substantial improvement over traditional GA and HF+RPA treatments. Dynamical correlation functions can be computed and are also substantially better than HF+RPA ones and obey well behaved sum rules.

arXiv:cond-mat/0006416•Physical Review Letters•Mar 19, 2001•85 citations

Scalar ground-state observables in the random phase approximation

Calvin W. Johnson, Ionel Stetcu

We calculate the ground-state expectation value of scalar observables in the matrix formulation of the random phase approximation (RPA). Our expression, derived using the quasiboson approximation, is a straightforward generalization of the RPA correlation energy. We test the reliability of our expression by comparing against full diagonalization in $0\ensuremath{\Elzxh}\ensuremath{\omega}$ shell-model spaces. In general the RPA values are an improvement over mean-field (Hartree-Fock) results, but are not always consistent with shell-model results. We also consider exact symmetries broken in the mean-field state and whether or not they are restored in RPA.

arXiv:nucl-th/0208025•Physical Review C•Dec 4, 2002•7 citations

Exact Single-Particle Green Functions of Fermi Systems Without Using Bosonization or Are Hartree-Fock and Random Phase Approximations 'Controlled Approximations' ?

Girish S. Setlur, Yia-Chung Chang

In this article, we revisit the question of the validity of Hartree-Fock and random-phase approximations. We show that there is a connection between the two and while the RPA as it is known in much of the physics literature is of limited validity, there is a generalised sense in which the random phase approximation is of much wider applicability including to systems that do not possess Fermi surfaces. The main conclusion is that the Hartree-Fock approximation is a mean-field idea applied to the density operator, and the random-phase approximation is a mean-field idea applied to the number operator. The generalised RPA is used to compute single-particle properties such as momentum distribution and spectral functions. It is found that we have to go beyond the generalised RPA and include fluctuations in the momentum distribution in order to recover a nonzero imaginary part of the one-particle self energy, which is also explicitly computed, all this in any number of spatial dimensions and no bosonization is needed.

arXiv:cond-mat/9810043•Oct 5, 1998•0 citations

SCF framework, HF stability and RPA correlation for Jordan-Wigner-transformed spin Hamiltonians on arbitrary coupling topologies

Shadan Ghassemi Tabrizi, Thomas M. Henderson, Thomas D. Kühne +1 more

Mapping spins to fermions via the Jordan-Wigner (JW) transformation can render mean-field (Hartree-Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering, because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-Algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytic orbital Hessian to diagnose HF stability and compute ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J1-J2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

arXiv:2601.13078•Jan 19, 2026•0 citations
The ground-state energy and static and dynamic correlation functions are investigated in the inhomogeneous-Hartree-Fock (IHF) plus random-phase-approximation (RPA) approach applied to a one-dimensional spinless-fermion model showing self-trapped doping states at the mean-field level. Results are compared with those obtained using homogeneous HF and exact diagonalization. RPA fluctuations added to the generally inhomogeneous-HF ground state allow the computation of dynamical correlation functions that compare well with exact diagonalization results. The RPA correction to the ground-state energy agrees well with the exact results at strong- and weak-coupling limits. We also compare it with a related quasiboson approach. The instability towards self-trapped behavior is signaled by a RPA mode with frequency approaching zero.
The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full $0\ensuremath{\Elzxh}\ensuremath{\omega}$ shell-model spaces we calculate the Hartree-Fock (HF)+RPA(\mathrm{HF})+\mathrm{RPA}(HF)+RPA binding energy, and compare it to exact diagonalization. We find that often, but not always, the HF+RPA\mathrm{HF}+\mathrm{RPA}HF+RPA gives a good approximation to the ``exact'' ground state energy. In those cases where the RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wave function. This weakens the reliability of the RPA for computing binding energies.
We present a detailed study of the time-dependent Gutzwiller approximation for the Hubbard model. The formalism, labeled GA+RPA, allows us to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). No restrictions are imposed on the charge and spin configurations which makes the method suitable for the calculation of linear excitations around symmetry-broken solutions. Well-behaved sum rules are obeyed as in the Hartree-Fock (HF) plus RPA approach. Analytical results for a two-site model and numerical results for charge-charge and current-current dynamical correlation functions in one and two dimensions are compared with exact and HF+RPA results, supporting the much better performance of GA+RPA with respect to conventional HF+RPA theory.
We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard model analogous to the time-dependent Hartree-Fock (HF) method. This new formalism incorporates ground state correlations of the random phase approximation (RPA) type beyond the GA. Static quantities like ground state energy and double occupancy are in excellent agreement with exact results in one dimension up to moderate coupling and in two dimensions for all couplings. We find a substantial improvement over traditional GA and HF+RPA treatments. Dynamical correlation functions can be computed and are also substantially better than HF+RPA ones and obey well behaved sum rules.
We calculate the ground-state expectation value of scalar observables in the matrix formulation of the random phase approximation (RPA). Our expression, derived using the quasiboson approximation, is a straightforward generalization of the RPA correlation energy. We test the reliability of our expression by comparing against full diagonalization in $0\ensuremath{\Elzxh}\ensuremath{\omega}$ shell-model spaces. In general the RPA values are an improvement over mean-field (Hartree-Fock) results, but are not always consistent with shell-model results. We also consider exact symmetries broken in the mean-field state and whether or not they are restored in RPA.
In this article, we revisit the question of the validity of Hartree-Fock and random-phase approximations. We show that there is a connection between the two and while the RPA as it is known in much of the physics literature is of limited validity, there is a generalised sense in which the random phase approximation is of much wider applicability including to systems that do not possess Fermi surfaces. The main conclusion is that the Hartree-Fock approximation is a mean-field idea applied to the density operator, and the random-phase approximation is a mean-field idea applied to the number operator. The generalised RPA is used to compute single-particle properties such as momentum distribution and spectral functions. It is found that we have to go beyond the generalised RPA and include fluctuations in the momentum distribution in order to recover a nonzero imaginary part of the one-particle self energy, which is also explicitly computed, all this in any number of spatial dimensions and no bosonization is needed.
Mapping spins to fermions via the Jordan-Wigner (JW) transformation can render mean-field (Hartree-Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering, because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-Algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytic orbital Hessian to diagnose HF stability and compute ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J1-J2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.