File  
Authors 
Kawamura, Mitsuaki
Institute for Solid State Physics, University of Tokyo
Yoshimi, Kazuyoshi
Institute for Solid State Physics, University of Tokyo
Motoyama, Yuichi
Institute for Solid State Physics, University of Tokyo
Misawa, Takahiro
Institute for Solid State Physics, University of Tokyo
Yamaji, Youhei
Department of Applied Physics, University of Tokyo
Todo, Synge
Department of Physics, University of Tokyo / Institute for Solid State Physics, University of Tokyo
Kawashima, Naoki
Institute for Solid State Physics, University of Tokyo
Sogabe, Tomohiro
Department of Applied Physics, Nagoya University

Keywords  Numerical linear algebra
Shifted linear equations
Krylov subspace method
Quantum lattice models

Abstract  We develop Kω, an opensource linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations (zkI−H)x(k)=b(k=0,1,2,…) for a given matrix H and a vector b, simultaneously. The leading order of the operational cost is the same as that for a single equation. The shift invariance of the Krylov subspace is the mathematical foundation of the shifted Krylov subspace methods. Applications in materials science are presented to demonstrate the advantages of the algorithm over the standard Krylov subspace methods such as the Lanczos method. We introduce benchmark calculations of (i) an excited (optical) spectrum and (ii) intermediate eigenvalues by the contour integral on the complex plane. In combination with the quantum lattice solver HΦ, Kω can realize parallel computation of excitation spectra and intermediate eigenvalues for various quantum lattice models.

Publisher  Elsevier

Content Type 
Journal Article

Link  
ISSN  00104655

Journal Title  Computer Physics Communications

Volume  258

Published Date  20210131

PublisherDOI  
Text Version 
Publisher

Rights  © 2020 The Authors. Published by Elsevier B.V. http://creativecommons.org/licenses/by/4.0/

Citation  Hoshi, Takeo. Kawamura, Mitsuaki. Yoshimi, Kazuyoshi. et al. Kω — Opensource library for the shifted Krylov subspace method of the form (zI−H)x=b. Computer Physics Communications. 258. 107536. 20210131.

Department 
Faculty of Engineering/Graduate School of Engineering

Language 
English

pii  S00104655(20)302551
