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
Submitted on: Sep 14, 2012, 15:07:22
Natural Sciences / Physics / Condensed Matter Physics
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 Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.
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