Localized density matrix minimization and linear-scaling algorithms
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© 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.
Published Version (Please cite this version)10.1016/j.jcp.2016.02.076
Publication InfoLai, 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.
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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.