d_{x^2-y^2}-wave superconductivity and the Hubbard model

TL;DR

This review discusses numerical studies of d_{x^2-y^2}-wave pairing in the 2D and 2-leg Hubbard models, highlighting microscopic processes and effective interactions relevant to high-T_c superconductivity.

Contribution

It provides a comprehensive review of quantum Monte Carlo and DMRG results, emphasizing the microscopic mechanisms behind d_{x^2-y^2}-wave pairing in the Hubbard model.

Findings

Effective pairing interaction is repulsive at (pi,pi)

Enhanced spectral weight near (pi,0) and (0,pi)

Conditions favoring d_{x^2-y^2}-wave pairing identified

Abstract

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 (pi,pi) momentum transfer and enhanced single-particle spectral weight near the (pi,0) and (0,pi) 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.