d-wave Pairing in the Two-Dimensional Hubbard Model

M. A. Baranov, M. Yu. Kagan

Mingpu Qin, Chia-Min Chung, Hao Shi +2 more

Thomas Pruschke, Thomas Maier, J. Keller +1 more

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.

H. C. Krahl, Jens Andreas Müller, CHRISTOF WETTERICH

Within the two-dimensional repulsive $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model, an attractive coupling in the $d$-wave-pairing channel is induced by antiferromagnetic fluctuations. We investigate this coupling using functional renormalization-group equations. The momentum-dependent $d$-wave coupling can be bosonized by the use of scale-dependent field transformations. We propose an effective coarse-grained model for the Hubbard model which is based on the exchange of antiferromagnetic and $d$-wave collective bosons.

Hiroki Tsuchiura, Yukio Tanaka, Yasunari Ushijima

Coexistence of the s and d x 2 - y 2 -wave ( d -wave) pairing is investigated in the two-dimensional (2-D) extended Hubbard model with on-site repulsive and inter-site attractive interactions using the mean-field approximation at T=0 K. The next-nearest-neighbor hopping effect can induce the coexistence of the s and d-wave pairing. It is found that in such a case, s + i d -wave pairing state becomes most stable.