Localized density matrix minimization and linear-scaling algorithms
Abstract
© 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 ℓ1 regularization 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 ℓ1 regularized 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 ℓ1 regularized
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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/14106Published Version (Please cite this version)
10.1016/j.jcp.2016.02.076Publication Info
Lai, R; & Lu, J (2016). Localized density matrix minimization and linear-scaling algorithms. Journal of Computational Physics, 315. pp. 194-210. 10.1016/j.jcp.2016.02.076. Retrieved from https://hdl.handle.net/10161/14106.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Jianfeng Lu
Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm
development for problems from computational physics, theoretical chemistry, materials
science and other related fields.More specifically, his current research focuses include:Electronic
structure and many body problems; quantum molecular dynamics; multiscale modeling
and analysis; rare events and sampling techniques.

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