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

Hartree theory for the negative- U extended Hubbard model: Ground state

S. Robaszkiewicz, R. Micnas, K. A. Chao

Published Oct 1, 1981• 64 citations
Publisher

Abstract

We have investigated the ground-state properties of the negative-$U$ extended Hubbard model in the weak-coupling regime with the Hartree theory formulated in terms of the Bogoliubov variational approach. While the pure phases of charge order (CO), singlet superconducting (SS), and nonordered can be solved analytically with a model density of states, the mixed phase of CO and SS requires numerical computation. The ground-state phase diagram is derived, and the order parameters and the chemical potential of the ground state are analyzed. The characteristic difference between the behaviors of the SS and the CO order parameters at very weak coupling suggests a complicated competition between various interactions. Present results are compared with those derived earlier for the strong-coupling regime.

DOI
10.1103/physrevb.24.4018

Related papers

Hartree theory for the negative- U extended Hubbard model. II. Finite temperature

S. Robaszkiewicz, R. Micnas, K. A. Chao

The zero-temperature Hartree theory is extended to finite temperature to investigate the phase diagram, the order parameters, and the chemical potential of the negative-$U$ extended Hubbard model in the weak-coupling regime. All the transitions between the charge-ordered, the singlet-superconducting, the mixed, and the nonordered phases are second order. In a special region of the parameter space, we discover the heat-charge-order process, which is the main source for the qualitative difference between the results of the present weak-coupling regime and the strong-coupling regime investigated earlier. Phenomena associated with the heat-charge order are compared to other work in which an effect similar to the heat-charge order exists.

Physical review. B, Condensed matter•Oct 1, 1982•68 citations

Finite Temperature Phase Diagram in the Half-Filled Extended Hubbard Model

Jian Zhong

The CDW-SDW transition in the half-filled extended Hubbard model is investigated with the broken-symmetry Hartree theory formulated in terms of the Bogoliubov variational approach. The finite temperature phase-diagram in the weak coupling regime is derived analytically with a model density of states. The results show that there exist charge-order and antiferromagnetic order, but no mixed phase exists at any temperatures.

Communications in Theoretical Physics•Sep 1, 1989•0 citations

Chemical potential and order parameter of extended Hubbard model with strong intra-atomic attraction

S. Robaszkiewicz, R. Micnas, K. A. Chao

We provide here the numerical solutions for the quasiparticle chemical potential and for the order parameters of the singlet-superconducting, the charge-ordered, and the mixed phases in an extended Hubbard model with strong intra-atomic attraction, based on the analysis of our previous paper.

Physical review. B, Condensed matter•Aug 1, 1981•59 citations

Electronic Structure of One-Dimensional Extended Hubbard Model

Kazuhiro Sano, Yoshiaki Ōno

We investigated the one-dimensional extended Hubbard model with the on-site interaction U and the nearest-neighbor interaction V by using the numerical diagonalization method. Assuming the Luttinger liquid relations, we obtained the phase diagram of the ground state on the U - V plane. In the weak coupling region, the phase diagram agrees with the result of g -ology. On the other hand, in the strong coupling region for V ≫∣ t ∣, a novel superconducting phase appears both for positive and negative U . We also investigated the charge gap and the spin gap. The results suggest that the superconducting phase extends over the Tomonaga-Luttinger region (without spin gap) and the Luther-Emery region (with spin gap).

Journal of the Physical Society of Japan•Apr 15, 1994•44 citations

Ground-state instabilities in a Hubbard-type chain with particular correlated hopping at non-half-filling

Weiting Chen, Jun Zhang, Hanqin Ding

At non-half-filling, a one-dimensional interacting electronic model (t–U–R) is studied analytically. The particular correlated hopping keeps particle–hole symmetry of the Hubbard model. Physically, the model involved is equivalent to an extended Hubbard chain incorporating a two-body (X) and a three-body (X˜) site-bond interactions with X˜=2X. The analysis of weak-coupling theory leads to the ground-state phase diagram, which consists of three types of metallic phases, characterized by the charge- (CDW) and spin-density-wave (SDW) and singlet-superconductivity (SS) instabilities.

Results in Physics•Apr 24, 2023•5 citations

Collective modes of the extended Hubbard model with negativeUand arbitrary electron density

T. Kostyrko, R. Micnas

By use of a diagrammatic method we determine the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. The energy of the collective modes, given by the poles of these response functions, is found to be a linear function of the wave vector (for small k and short-range intersite interaction) with the velocity interpolating smoothly between the weak- (\ensuremath{\propto}2zt, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\ll}2zt) and strong-coupling (\ensuremath{\propto}${\mathit{zt}}^{2}$/\ensuremath{\Vert}U\ensuremath{\Vert}, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}2zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong-coupling limit. The numerical analysis for a two-dimensional (2D) square lattice shows the occurrence of a rotonlike minima near the zone boundary. In the weak-coupling regime we find that apart from a commensurate charge-density-wave (CDW) instability, an increase in the intersite Coulomb repulsion can give rise to a CDW incommensurate with the lattice period, away from half-filling. The resulting phase diagram for the 2D square lattice, including a singlet superconducting ground state, electronic-droplet formation, and CDW's, is determined. Finally, the effects of a long-range Coulomb interaction are analyzed briefly and it is shown that the energy of collective excitations evolves smoothly from the weak- to the strong-coupling limit for a 2D lattice.

Physical review. B, Condensed matter•Nov 1, 1992•41 citations
We have investigated the ground-state properties of the negative-UUU extended Hubbard model in the weak-coupling regime with the Hartree theory formulated in terms of the Bogoliubov variational approach. While the pure phases of charge order (CO), singlet superconducting (SS), and nonordered can be solved analytically with a model density of states, the mixed phase of CO and SS requires numerical computation. The ground-state phase diagram is derived, and the order parameters and the chemical potential of the ground state are analyzed. The characteristic difference between the behaviors of the SS and the CO order parameters at very weak coupling suggests a complicated competition between various interactions. Present results are compared with those derived earlier for the strong-coupling regime.
The zero-temperature Hartree theory is extended to finite temperature to investigate the phase diagram, the order parameters, and the chemical potential of the negative-UUU extended Hubbard model in the weak-coupling regime. All the transitions between the charge-ordered, the singlet-superconducting, the mixed, and the nonordered phases are second order. In a special region of the parameter space, we discover the heat-charge-order process, which is the main source for the qualitative difference between the results of the present weak-coupling regime and the strong-coupling regime investigated earlier. Phenomena associated with the heat-charge order are compared to other work in which an effect similar to the heat-charge order exists.
We investigated the one-dimensional extended Hubbard model with the on-site interaction U and the nearest-neighbor interaction V by using the numerical diagonalization method. Assuming the Luttinger liquid relations, we obtained the phase diagram of the ground state on the U - V plane. In the weak coupling region, the phase diagram agrees with the result of g -ology. On the other hand, in the strong coupling region for V ≫∣ t ∣, a novel superconducting phase appears both for positive and negative U . We also investigated the charge gap and the spin gap. The results suggest that the superconducting phase extends over the Tomonaga-Luttinger region (without spin gap) and the Luther-Emery region (with spin gap).
At non-half-filling, a one-dimensional interacting electronic model (t–U–R) is studied analytically. The particular correlated hopping keeps particle–hole symmetry of the Hubbard model. Physically, the model involved is equivalent to an extended Hubbard chain incorporating a two-body (X) and a three-body (X˜) site-bond interactions with X˜=2X. The analysis of weak-coupling theory leads to the ground-state phase diagram, which consists of three types of metallic phases, characterized by the charge- (CDW) and spin-density-wave (SDW) and singlet-superconductivity (SS) instabilities.
By use of a diagrammatic method we determine the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. The energy of the collective modes, given by the poles of these response functions, is found to be a linear function of the wave vector (for small k and short-range intersite interaction) with the velocity interpolating smoothly between the weak- (\ensuremath{\propto}2zt, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\ll}2zt) and strong-coupling (\ensuremath{\propto}zt2{\mathit{zt}}^{2}zt2/\ensuremath{\Vert}U\ensuremath{\Vert}, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}2zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong-coupling limit. The numerical analysis for a two-dimensional (2D) square lattice shows the occurrence of a rotonlike minima near the zone boundary. In the weak-coupling regime we find that apart from a commensurate charge-density-wave (CDW) instability, an increase in the intersite Coulomb repulsion can give rise to a CDW incommensurate with the lattice period, away from half-filling. The resulting phase diagram for the 2D square lattice, including a singlet superconducting ground state, electronic-droplet formation, and CDW's, is determined. Finally, the effects of a long-range Coulomb interaction are analyzed briefly and it is shown that the energy of collective excitations evolves smoothly from the weak- to the strong-coupling limit for a 2D lattice.