Renormalization-group analysis of the two-dimensional Hubbard model

被引:291
作者
Halboth, CJ [1 ]
Metzner, W [1 ]
机构
[1] Rhein Westfal TH Aachen, Inst Theoret Phys C, D-52056 Aachen, Germany
来源
PHYSICAL REVIEW B | 2000年 / 61卷 / 11期
关键词
D O I
10.1103/PhysRevB.61.7364
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Salmhofer [Commun. Math. Phys. 194, 249 (1998)] recently developed a new renormalization-group method for interacting Fermi systems, where the complete flow from the bare action of a microscopic model to the effective low-energy action, as a function of a continuously decreasing infrared cutoff, is given by a differential flow equation which is local in the flow parameter. We apply this approach to the repulsive two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping amplitudes. The how equation for the effective interaction is evaluated numerically on a one-loop level. The effective interactions diverge at a finite-energy scale which is exponentially small for small bare interactions. To analyze the nature of the instabilities signaled by the diverging interactions we extend Salmhofer's renormalization group for the calculation of susceptibilities. We compute the singlet superconducting susceptibilities for various pairing symmetries, and also charge- and spin-density susceptibilities. Depending on the choice of the model parameters (hopping amplitudes, interaction strength, and band filling) we find commensurate and incommensurate antiferromagnetic instabilities or d-wave superconductivity as leading instability. We present the resulting phase diagram in the vicinity of half-filling, and also results for the density dependence of the critical energy scale.
引用
收藏
页码:7364 / 7377
页数:14
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