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

Random-phase-approximation approach to collective modes around inhomogeneous Hartree-Fock states: One-dimensional doped Hubbard model

Kenji Yonemitsu, I. Batistić, A. R. Bishop

Published Aug 1, 1991• 21 citations
Publisher

Abstract

All the linear excitations are calculated in the random-phase approximation around a doped inhomogeneous Hartree-Fock state as well as the undoped uniform antiferromagnetic state in the one-dimensional Hubbard model. Upon doping, shape modes appear, localized around an introduced hole, as well as some ``shake-off'' branches related to combinations of local and extended Hartree-Fock orbitals. These modes are in addition to spin wave and ultragap branches in the pure antiferromagnetic state. Some characteristics of the shape modes are similar to bare processes in the t-t'-J model derived from the Hubbard model at strong coupling. Spectral weights in different susceptibility channels are calculated and shown to have peaks in low-energy regions, arising from specific shape modes.

DOI
10.1103/physrevb.44.2652

Related papers

Collective excitation spectrum of a disordered Hubbard model

Yolande H Szczech, Michael A Tusch, David E Logan

We study the collective excitation spectrum of a d = 3 site-disordered Anderson - Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree - Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder - interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.

arXiv:cond-mat/9805132•Journal of Physics Condensed Matter•Nov 3, 1997•2 citations

Spin waves in the spiral phase of a doped antiferromagnet: a strong-coupling approach

N. Dupuis

We study spin fluctuations in the spiral phase of the two-dimensional Hubbard model at low doping on the basis of the spin-particle-hole coherent-state path integral. In the strong correlation limit, we obtain an analytical expression of the spin-wave excitations over the entire Brillouin zone except in the vicinity of ${\bf q}=0$. We discuss the validity of the Hartree-Fock and random-phase approximations in the strong-coupling limit, and compare our results with previous numerical and analytical calculations. Although the spiral phase is unstable, as shown by a negative mean-field compressibility and the presence of imaginary spin-fluctuation modes, we expect the short-wavelength fluctuation modes (with real energies) to survive in the actual ground-state of the system.

arXiv:cond-mat/0105063•May 3, 2001•0 citations

Excitations and response functions of the doped two-dimensional Hubbard model: A random-phase-approximation anaylsis

F. Guinea, Enrique Louis, José Antonio Vergés

We calculate the excitation spectrum and the response functions of the textures induced by doping in the half-filled Hubbard model. Localized states appear within the antiferromagnetic gap. The spin-wave spectrum is distorted, and shifted towards lower energies; its total strength is reduced. The antiferromagnetic peak at (\ensuremath{\pi},\ensuremath{\pi}) is broadened and moves to higher energies. Charge excitations appear at low energies and mix with the spin waves. Their polarization induces screened interactions that can overcome the initial, repulsive, ones. The general features of the results cannot be described in conventional-Fermi-liquid or, alternatively, insulator terms.

Physical review. B, Condensed matter•Mar 1, 1992•14 citations

Hartree Fock and RPA studies of the Hubbard model

F. Guinea, E. Louis, José Antonio Vergés

The applicability of the Hartree-Fock and random phase approximations to models of strongly correlated electrons is discussed. The 2D Hubbard model is analyzed. An antiferromagnetic phase (at half filling) and Fermi liquid behavior (at low electron densities) are found. In addition, the system shows an unconventional regime near half filling. It is characterized by the formation of spin and charge textures. Local magnetic moments and spin waves are also present, and the quasiparticle pole at the Fermi energy vanishes. The charge excitation spectrum is gapless. The overall features resemble those of the 1D Luttinger liquid.

arXiv:cond-mat/9401057•Jan 26, 1994•0 citations

Phase diagram of the two-dimensional disordered Hubbard model in the Hartree-Fock approximation

Chandan Dasgupta, J. W. Halleý

Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)--\ensuremath{\delta}(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.

Physical review. B, Condensed matter•Jan 1, 1993•21 citations

Influence of spin-wave excitations on the ferromagnetic phase diagram in the Hubbard model

W. Rumsch, Wolfgang Nolting

The subject of the present paper is the theoretical description of collective electronic excitations, i.e., spin waves, in the Hubbard model. Starting with the widely used random-phase approximation, which combines Hartree-Fock theory with the summation of the two-particle ladder, we extend the theory to a more sophisticated single particle approximation, namely, the spectral-density ansatz. Doing so we have to introduce a ``screened'' Coulomb interaction rather than the bare Hubbard interaction in order to obtain physically reasonable spinwave dispersions. The discussion following the technical procedure shows that comparison of standard RPA with our new approximation reduces the occurrence of a ferromagnetic phase further with respect to the phase diagrams delivered by the single particle theories.

arXiv:cond-mat/0209480•Physical review. B, Condensed matter•Nov 25, 2002•7 citations
All the linear excitations are calculated in the random-phase approximation around a doped inhomogeneous Hartree-Fock state as well as the undoped uniform antiferromagnetic state in the one-dimensional Hubbard model. Upon doping, shape modes appear, localized around an introduced hole, as well as some ``shake-off'' branches related to combinations of local and extended Hartree-Fock orbitals. These modes are in addition to spin wave and ultragap branches in the pure antiferromagnetic state. Some characteristics of the shape modes are similar to bare processes in the t-t'-J model derived from the Hubbard model at strong coupling. Spectral weights in different susceptibility channels are calculated and shown to have peaks in low-energy regions, arising from specific shape modes.
We study the collective excitation spectrum of a d = 3 site-disordered Anderson - Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree - Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder - interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.
We study spin fluctuations in the spiral phase of the two-dimensional Hubbard model at low doping on the basis of the spin-particle-hole coherent-state path integral. In the strong correlation limit, we obtain an analytical expression of the spin-wave excitations over the entire Brillouin zone except in the vicinity of q=0{\bf q}=0q=0. We discuss the validity of the Hartree-Fock and random-phase approximations in the strong-coupling limit, and compare our results with previous numerical and analytical calculations. Although the spiral phase is unstable, as shown by a negative mean-field compressibility and the presence of imaginary spin-fluctuation modes, we expect the short-wavelength fluctuation modes (with real energies) to survive in the actual ground-state of the system.
We calculate the excitation spectrum and the response functions of the textures induced by doping in the half-filled Hubbard model. Localized states appear within the antiferromagnetic gap. The spin-wave spectrum is distorted, and shifted towards lower energies; its total strength is reduced. The antiferromagnetic peak at (\ensuremath{\pi},\ensuremath{\pi}) is broadened and moves to higher energies. Charge excitations appear at low energies and mix with the spin waves. Their polarization induces screened interactions that can overcome the initial, repulsive, ones. The general features of the results cannot be described in conventional-Fermi-liquid or, alternatively, insulator terms.
The applicability of the Hartree-Fock and random phase approximations to models of strongly correlated electrons is discussed. The 2D Hubbard model is analyzed. An antiferromagnetic phase (at half filling) and Fermi liquid behavior (at low electron densities) are found. In addition, the system shows an unconventional regime near half filling. It is characterized by the formation of spin and charge textures. Local magnetic moments and spin waves are also present, and the quasiparticle pole at the Fermi energy vanishes. The charge excitation spectrum is gapless. The overall features resemble those of the 1D Luttinger liquid.
Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)--\ensuremath{\delta}(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.
The subject of the present paper is the theoretical description of collective electronic excitations, i.e., spin waves, in the Hubbard model. Starting with the widely used random-phase approximation, which combines Hartree-Fock theory with the summation of the two-particle ladder, we extend the theory to a more sophisticated single particle approximation, namely, the spectral-density ansatz. Doing so we have to introduce a ``screened'' Coulomb interaction rather than the bare Hubbard interaction in order to obtain physically reasonable spinwave dispersions. The discussion following the technical procedure shows that comparison of standard RPA with our new approximation reduces the occurrence of a ferromagnetic phase further with respect to the phase diagrams delivered by the single particle theories.