期刊
MULTISCALE MODELING & SIMULATION
卷 16, 期 3, 页码 1392-1410出版社
SIAM PUBLICATIONS
DOI: 10.1137/17M1129696
关键词
Wannier functions; localization; compression; density matrix; band structure; disentanglement
资金
- National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship [DMS-1606277]
- U.S. Department of Energy [DE-SC0017867]
- National Science Foundation [DMS-1652330]
- Alfred P. Sloan fellowship
The Wannier localization problem in quantum physics is mathematically analogous to finding a localized representation of a subspace corresponding to a nonlinear eigenvalue problem. While Wannier localization is well understood for insulating materials with isolated eigenvalues, less is known for metallic systems with entangled eigenvalues. Currently, the most widely used method for treating systems with entangled eigenvalues is to first obtain a reduced subspace (often referred to as disentanglement) and then to solve the Wannier localization problem by treating the reduced subspace as an isolated system. This is a multiobjective nonconvex optimization procedure, and its solution can depend sensitively on the initial guess. We propose a new method to solve the Wannier localization problem, avoiding the explicit use of an optimization procedure. Our method is robust and efficient, relies on few tunable parameters, and provides a unified framework for addressing problems with isolated and entangled eigenvalues.
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