期刊
PHYSICAL REVIEW LETTERS
卷 121, 期 3, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.121.032501
关键词
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资金
- U.S. Department of Energy [DE-FG02-03ER41260]
- National Science Foundation, Army Research Laboratory
- Office of Naval Research
- Air Force Office of Scientific Research
- Department of Transportation
- XDATA Program of the Defense Advanced Research Projects Agency administered through the Air Force Research Laboratory [FA8750-12-C-0323]
- Natural Sciences and Engineering Research Council of Canada
- Canada Foundation for Innovation
A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous efficient methods developed for this task, but they generally fail when some control parameter in the Hamiltonian matrix exceeds some threshold value. In this Letter we present a new technique called eigenvector continuation that can extend the reach of these methods. The key insight is that while an eigenvector resides in a linear space with enormous dimensions, the eigenvector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold. We prove this statement using analytic function theory and propose an algorithm to solve for the extremal eigenvectors. We benchmark the method using several examples from quantum many-body theory.
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