Renormalization-group acceleration of self-consistent field solutions: Two-dimensional Hubbard model

Momentum- and frequency-dependent self-consistent field theories provide a potentially powerful tool for analyzing condensed-matter models for interacting electrons. Such theories generally require the solution of multidimensional integral equations. Solutions are limited by demands on computational time and storage, which increase rapidly for calculation of low-temperature properties. A renormalization-group technique which allows the sequential elimination of regions of high frequency and momentum is presented in detail, and is then applied to the solution of the fluctuation exchange approximation for the two-dimensional Hubbard model. Effective meshes with as many as 10⁴ frequencies and 512² k points can be analyzed on a vector supercomputer using this approach. As a sample application, it is demonstrated that the fluctuation exchange approximation exhibits non-Fermi liquid behavior near half filling for sufficiently large interaction strengths.