Pierre Carrier, Jok M. Tang, Yousef Saad, James K. Freericks. Lanczos-based Low-rank Correction Method for Solving the Dyson Equation in Inhomogenous Dynamical Mean-field Theory


Natural Sciences / Physics / Condensed Matter Physics

Submitted on: Sep 14, 2012, 15:07:22

Description: Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each lattice site from the corresponding local self-energy. We present a new efficient algorithm, the Lanczos-based low-rank algorithm, for the calculation of the inverse of a large sparse matrix which yields this local (imaginary time) Green's function. The Lanczos-based low-rank algorithm is based on a domain decomposition viewpoint, but avoids explicit calculation of Schur complements and relies instead on low-rank matrix approximations derived from the Lanczos algorithm, for solving the Dyson equation.

The abstract of this article will be published in the September 2012 issue of "Intellectual Archive Bulletin", ISSN 1929-1329.

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