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:cond-mat/9712073

Asymptotic expansion of the ground state energy of half-filled Hubbard model

Minoru Takahashi

Published Dec 5, 1997• 0 citations
arXivHTMLPDF

Abstract

This paper was withdrawn by the author because the results already appeared in PRB 20, 4756 (1979).
DOI
10.48550/arxiv.cond-mat/9712073

Related papers

Ground-state energy of the half-filled one-dimensional Hubbard model

Eleftherios N. Economou, P. Poulopoulos

The exact result of Lieb and Wu is recast as an asymptotic series in the small-U limit. This series permits comparisons with a recent approximate method and with the perturbation expansion.Received 25 July 1979DOI:https://doi.org/10.1103/PhysRevB.20.4756©1979 American Physical Society

Physical review. B, Condensed matter•Dec 1, 1979•24 citations

Ground state of the half-filled extended Hubbard model beyond the Hartree-Fock approximation

Andrzej M. Oleś, R. Micnas, S. Robaszkiewicz +1 more

Physics Letters A•May 1, 1984•13 citations

On the scaling limit of the 1D Hubbard model at half-filling

Ezer Melzer

arXiv:cond-mat/9410043•Nuclear Physics B•Jun 1, 1995•24 citations

Large-Uexpansions for the Hubbard model atT=0. II

J. Oitmaa, Yang Jie, Jon Henderson +1 more

We investigate the ground state of the Hubbard model in one and two dimensions. Long perturbation expansions in t/U, i.e., about the atomic limit, are computed for the ground-state energy of finite lattices with N\ensuremath{\le}10 for arbitrary electron density. We also extend the series for the one-dimensional infinite lattice by expanding the Bethe-ansatz equations. Pad\'e-approximant analysis of the series shows a distribution of singularities that varies dramatically with the electron density n. We also investigate the effect of inclusion of next-nearest-neighbor hopping. This appears to have little effect at half-filling but is significant away from half-filling.

Physical review. B, Condensed matter•Sep 1, 1993•1 citation

Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Chia‐Wei Yang, ARMEN N. KOCHARIAN, Y. L. Chiang

The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.

Journal of Physics Condensed Matter•Aug 2, 2000•24 citations

The Two Dimensional Hubbard Model at Half-Filling. I. Convergent Contributions

Vincent Rivasseau

Journal of Statistical Physics•Feb 1, 2002•17 citations
We investigate the ground state of the Hubbard model in one and two dimensions. Long perturbation expansions in t/U, i.e., about the atomic limit, are computed for the ground-state energy of finite lattices with N\ensuremath{\le}10 for arbitrary electron density. We also extend the series for the one-dimensional infinite lattice by expanding the Bethe-ansatz equations. Pad\'e-approximant analysis of the series shows a distribution of singularities that varies dramatically with the electron density n. We also investigate the effect of inclusion of next-nearest-neighbor hopping. This appears to have little effect at half-filling but is significant away from half-filling.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.