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

Generalized Hubbard Hamiltonian: Renormalization-group approach

Sergio Alejandro Cannas, Francisco A. Tamarit, Constantino Tsallis

Published May 1, 1992• 4 citations
Publisher

Abstract

We study a generalized Hubbard Hamiltonian which is closed within the framework of a quantum real-space renormalization group, which replaces the d-dimensional hypercubic lattice by a diamondlike lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled-band case for d=2 and d=3. Some evidence for superconductivity is presented.

DOI
10.1103/physrevb.45.10496

Related papers

Real-space scaling methods applied to the one-dimensional extended Hubbard model. I. The real-space renormalization-group method

B. Fourcade, G. Spronken

The real-space renormalization-group method is applied to the one-dimensional extended Hubbard model. It is shown that in the half-filled-band case, the phase diagram consists of two phases and that the transition from the spin-ordered phase to the charge-ordered phase is continuous, a result which differs from that obtained previously from the broken-symmetry Hartree-Fock approximation.

Physical review. B, Condensed matter•May 1, 1984•42 citations

Real-space renormalization-group study of the two-dimensional Hubbard model

Jesús Pérez-Conde, Pierre M. Pfeuty

The one-band two-dimensional Hubbard Hamiltonian is analyzed using a real-space renormalization-group block method. The renormalization-group method, previously applied to the one-dimensional case has been extended to two dimensions. It is also shown how to avoid the proliferation of new terms during the process if the shape of the blocks and the symmetries of the kept states are chosen conveniently. We characterize the ground state by its energy per site, the gap of charge excitations, the double occupancy, and the effective hopping. The system shows an insulating behavior in the case of half filling for all nonzero interaction parameter, U, if the hopping is isotropic (${\mathit{t}}_{\mathit{y}}$=${\mathit{t}}_{\mathit{x}}$); that is to say, the gap opens for all positive U, as in the one-dimensional case. If the hopping anisotropy, \ensuremath{\alpha}=${\mathit{t}}_{\mathit{y}}$/${\mathit{t}}_{\mathit{x}}$, is different from the unity and zero the ground state is a conductor up to a critical value (U/t${)}_{\mathit{c}1}$, which depends on \ensuremath{\alpha}. We have analyzed in the same way another filling, n=7/9. The system behaves as a conductor, paramagnetic up to a value (U/t${)}_{\mathit{c}2}$\ensuremath{\sim}2 and weakly ferromagnetic for higher values of U.

Physical review. B, Condensed matter•Jan 1, 1993•16 citations

The generalized Hubbard model in one dimension: a renormalization group study

B Bhattacharyya, Sanchita Sil

We have modified an existing real space renormalization group scheme to remove some physically inconsistent features and used the rectified method to study the ground state of the one-dimensional Hubbard model with nearest-neighbour repulsion and the bond-charge interaction for half filling. For the nearest-neighbour interaction we find a phase diagram which agrees nicely with the Monte Carlo results. For the case of bond-charge interaction we have reproduced some available exact results and found some interesting information in the parameter regime where no exact solution is available.

Journal of Physics Condensed Matter•Aug 14, 1995•5 citations

Renormalization group analysis of the one-dimensional extended Hubbard model

M. Ménard, C. Bourbonnais

The phase diagram of the one-dimensional extended Hubbard model at half filling is investigated by a weak-coupling renormalization group method applicable beyond the usual continuum limit for the electron spectrum and coupling constants. We analyze the influence of irrelevant momentum dependent interactions on asymptotic properties of correlation functions and the nature of dominant phases for the lattice model under study.

arXiv:1009.4181•Physical Review B•Feb 16, 2011•17 citations

Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study

Masaki Tezuka, Ryotaro Arita, Hideo Aoki

Phase diagram of the Hubbard-Holstein model in the coexistence of electron-electron and electron-phonon interactions has been theoretically obtained with the density-matrix renormalization group method for one-dimensional systems, where an improved warm-up (the recursive sweep) procedure has enabled us to calculate various correlation functions. We have examined the cases of (i) the systems half-filled by electrons for the full parameter space spanned by the electron-electron and electron-phonon coupling constants and the phonon frequency, (ii) non-half-filled system, and (iii) trestle lattice. For (i), we have detected a region where both the charge and on-site pairing correlations decay with power laws in real space, which suggests a metallic behavior. While pairing correlations are not dominant in (i), we have found that they become dominant as the system is doped in (ii) or as the electronic band structure is modified (with a broken electron-hole symmetry) in (iii) in certain parameter regions.

arXiv:0707.3197•Physical Review B•Oct 19, 2007•78 citations

Phase diagrams of the two-dimensional extended Hubbard model: a comprehensive functional renormalization group study

Arooj Aslam, Yuan-Yuan Xiang, Cheng-Wei Li +2 more

Abstract Using the singular-mode functional renormalization group method, we studied the doping-dependent phase diagram of the two-dimensional extended Hubbard model on square lattice. At half-filling, a variety of states strongly compete, including spin-density wave, charge-density wave, phase separation, as well as d -wave and s -wave superconductivity (SC). Upon electron doping, the system exhibits a strong preference for superconducting states. At slight dopings, the spin-density wave phase is strongly suppressed, and d -wave SC region expands into positive U , V region. At moderate dopings, a region of degenerated p -wave superconductivities emerge for positive U and negative V . Our results demonstrate how doping tunes the dominant fluctuations, suppressing density waves and stabilizing unconventional superconducting states in two dimensions.

Journal of Physics Condensed Matter•Dec 23, 2025•0 citations
We study a generalized Hubbard Hamiltonian which is closed within the framework of a quantum real-space renormalization group, which replaces the d-dimensional hypercubic lattice by a diamondlike lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled-band case for d=2 and d=3. Some evidence for superconductivity is presented.
The one-band two-dimensional Hubbard Hamiltonian is analyzed using a real-space renormalization-group block method. The renormalization-group method, previously applied to the one-dimensional case has been extended to two dimensions. It is also shown how to avoid the proliferation of new terms during the process if the shape of the blocks and the symmetries of the kept states are chosen conveniently. We characterize the ground state by its energy per site, the gap of charge excitations, the double occupancy, and the effective hopping. The system shows an insulating behavior in the case of half filling for all nonzero interaction parameter, U, if the hopping is isotropic (ty{\mathit{t}}_{\mathit{y}}ty​=tx{\mathit{t}}_{\mathit{x}}tx​); that is to say, the gap opens for all positive U, as in the one-dimensional case. If the hopping anisotropy, \ensuremath{\alpha}=ty{\mathit{t}}_{\mathit{y}}ty​/tx{\mathit{t}}_{\mathit{x}}tx​, is different from the unity and zero the ground state is a conductor up to a critical value (U/t)c1{)}_{\mathit{c}1})c1​, which depends on \ensuremath{\alpha}. We have analyzed in the same way another filling, n=7/9. The system behaves as a conductor, paramagnetic up to a value (U/t)c2{)}_{\mathit{c}2})c2​\ensuremath{\sim}2 and weakly ferromagnetic for higher values of U.
We have modified an existing real space renormalization group scheme to remove some physically inconsistent features and used the rectified method to study the ground state of the one-dimensional Hubbard model with nearest-neighbour repulsion and the bond-charge interaction for half filling. For the nearest-neighbour interaction we find a phase diagram which agrees nicely with the Monte Carlo results. For the case of bond-charge interaction we have reproduced some available exact results and found some interesting information in the parameter regime where no exact solution is available.
Phase diagram of the Hubbard-Holstein model in the coexistence of electron-electron and electron-phonon interactions has been theoretically obtained with the density-matrix renormalization group method for one-dimensional systems, where an improved warm-up (the recursive sweep) procedure has enabled us to calculate various correlation functions. We have examined the cases of (i) the systems half-filled by electrons for the full parameter space spanned by the electron-electron and electron-phonon coupling constants and the phonon frequency, (ii) non-half-filled system, and (iii) trestle lattice. For (i), we have detected a region where both the charge and on-site pairing correlations decay with power laws in real space, which suggests a metallic behavior. While pairing correlations are not dominant in (i), we have found that they become dominant as the system is doped in (ii) or as the electronic band structure is modified (with a broken electron-hole symmetry) in (iii) in certain parameter regions.
Abstract Using the singular-mode functional renormalization group method, we studied the doping-dependent phase diagram of the two-dimensional extended Hubbard model on square lattice. At half-filling, a variety of states strongly compete, including spin-density wave, charge-density wave, phase separation, as well as d -wave and s -wave superconductivity (SC). Upon electron doping, the system exhibits a strong preference for superconducting states. At slight dopings, the spin-density wave phase is strongly suppressed, and d -wave SC region expands into positive U , V region. At moderate dopings, a region of degenerated p -wave superconductivities emerge for positive U and negative V . Our results demonstrate how doping tunes the dominant fluctuations, suppressing density waves and stabilizing unconventional superconducting states in two dimensions.