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/0409669

Absence of superconductivity in the 2D Hubbard model

Thomas Maier, Mark Jarrell, T. C. Schulthess, James B. White

Published Sep 24, 2004• 0 citations
arXivHTMLPDF

Abstract

After receiving a number of comments and reviews from our colleagues who have suggested that our results could be greatly improved by other methods of extrapolation, we have decided to withdraw our paper entitled "Absence of superconductivity in the 2D Hubbard model" until we can perform these calculations.
DOI
10.48550/arxiv.cond-mat/0409669

Related papers

Does the 2D Hubbard Model Really Show d -Wave Superconductivity?

Gang Su

Some issues concerning the question if the two-dimensional Hubbard model really show d-wave superconductivity are briefly discussed.

arXiv:cond-mat/0104388•Physical Review Letters•Apr 16, 2001•8 citations

d x 2 - y 2 superconductivity and the Hubbard model

N. Bulut

The numerical studies of d x 2 - y 2 -wave pairing in the two-dimensional (2D) and the 2-leg Hubbard models are reviewed. For this purpose, the results obtained from the determinantal Quantum Monte Carlo and the Density-Matrix Renormalization-Group calculations are presented. These are calculations which were motivated by the discovery of the high- T c cuprates. In this review, the emphasis is placed on the microscopic many-body processes which are responsible for the d x 2 - y 2 -wave pairing correlations observed in the 2D and the 2-leg Hubbard models. In order to gain insight into these processes, the results on the effective pairing interaction as well as the magnetic, density and the single-particle excitations will be reviewed. In addition, comparisons will be made with the other numerical approaches to the Hubbard model and the numerical results on the t - J model. The results reviewed here indicate that an effective pairing interaction which is repulsive at ( ~ , ~ ) momentum transfer, and enhanced single-particle spectral weight near the ( ~ ,0) and (0, ~ ) points of the Brillouin zone, create optimum conditions for d x 2 - y 2 -wave pairing. These are two effects which act to enhance the d x 2 - y 2 -wave pairing correlations in the Hubbard model. Finding additional ways is an active research problem.

arXiv:cond-mat/0207186•Advances In Physics•Nov 1, 2002•88 citations

Pairing in the two-dimensional Hubbard model: An exact diagonalization study

H. Q. Lin, J. E. Hirsch, Douglas J. Scalapino

We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order ${U}^{2}$ contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.

Physical review. B, Condensed matter•May 1, 1988•80 citations

Superconductivity in the 2D Hubbard model

S. S. Kancharla, Massimo Capone, Marcello Civelli +3 more

Bulletin of the American Physical Society•Mar 24, 2005•0 citations

Comment on arXiv:0811.1575 entitled "Quantum phase transitions in the Hubbard model on triangular lattice" by T. Yoshioka, A. Koga and N. Kawakami

Shinji Watanabe, T. Mizusaki, Masatoshi Imada

We show that the phase boundary between the paramagnetic metal and the nonmagnetic Mott insulator for the Hubbard model on a triangular lattice obtained by Yoshioka et al. in arXiv:0811.1575 does not correctly represent that of the thermodynamic limit but is an artifact of the 6 by 6 lattice they rely on. After the system size extrapolation, the phase boundary is located at U/t=5.2 as proposed by Morita et al., J. Phys. Soc. Jpn. 71 (2008) 2109 and in contrast to Yoshioka et al. Here, U is the onsite Coulomb repulsion and t is the nearest-neighbor transfer.

arXiv:0811.3718•Nov 22, 2008•1 citation

On the existence of superconductivity in the Hubbard model

N. N. Bogolyubov, V. A. Moskalenko

Theoretical and Mathematical Physics•Jan 1, 1991•30 citations
The numerical studies of d x 2 - y 2 -wave pairing in the two-dimensional (2D) and the 2-leg Hubbard models are reviewed. For this purpose, the results obtained from the determinantal Quantum Monte Carlo and the Density-Matrix Renormalization-Group calculations are presented. These are calculations which were motivated by the discovery of the high- T c cuprates. In this review, the emphasis is placed on the microscopic many-body processes which are responsible for the d x 2 - y 2 -wave pairing correlations observed in the 2D and the 2-leg Hubbard models. In order to gain insight into these processes, the results on the effective pairing interaction as well as the magnetic, density and the single-particle excitations will be reviewed. In addition, comparisons will be made with the other numerical approaches to the Hubbard model and the numerical results on the t - J model. The results reviewed here indicate that an effective pairing interaction which is repulsive at ( ~ , ~ ) momentum transfer, and enhanced single-particle spectral weight near the ( ~ ,0) and (0, ~ ) points of the Brillouin zone, create optimum conditions for d x 2 - y 2 -wave pairing. These are two effects which act to enhance the d x 2 - y 2 -wave pairing correlations in the Hubbard model. Finding additional ways is an active research problem.
We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order U2{U}^{2}U2 contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.
We show that the phase boundary between the paramagnetic metal and the nonmagnetic Mott insulator for the Hubbard model on a triangular lattice obtained by Yoshioka et al. in arXiv:0811.1575 does not correctly represent that of the thermodynamic limit but is an artifact of the 6 by 6 lattice they rely on. After the system size extrapolation, the phase boundary is located at U/t=5.2 as proposed by Morita et al., J. Phys. Soc. Jpn. 71 (2008) 2109 and in contrast to Yoshioka et al. Here, U is the onsite Coulomb repulsion and t is the nearest-neighbor transfer.