Localized density matrix minimization and linear-scaling algorithms

Published

Journal Article

© 2016 Elsevier Inc. We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise ℓ1regularization to the free energy of the quantum system. Based on the fact that the density matrix decays exponentially away from the diagonal for insulating systems or systems at finite temperature, the proposed ℓ1regularized variational method provides an effective way to approximate the original quantum system. We provide theoretical analysis of the approximation behavior and also design convergence guaranteed numerical algorithms based on Bregman iteration. More importantly, the ℓ1regularized system naturally leads to localized density matrices with banded structure, which enables us to develop approximating algorithms to find the localized density matrices with computation cost linearly dependent on the problem size.

Full Text

Duke Authors

Cited Authors

  • Lai, R; Lu, J

Published Date

  • June 15, 2016

Published In

Volume / Issue

  • 315 /

Start / End Page

  • 194 - 210

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/j.jcp.2016.02.076

Citation Source

  • Scopus