Densities of states for disordered systems from free probability
Name
Welborn-2013-Densities of states.pdf
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Author(s)
Chen, Jiahao
Van Voorhis, Troy
Welborn, Matthew Gregory
Date Issued
November 2013
Journal
Physical Review B
Publisher
American Physical Society
Citation
Welborn, Matthew, Jiahao Chen, and Troy Van Voorhis. “Densities of States for Disordered Systems from Free Probability.” Phys. Rev. B 88, no. 20 (November 2013). © 2013 American Physical Society
Version
Final published version
Abstract
We investigate how free probability allows us to approximate the density of states in tight-binding models of disordered electronic systems. Extending our previous studies of the Anderson model in one dimension with nearest-neighbor interactions [Chen et al., Phys. Rev. Lett. 109, 036403 (2012)], we find that free probability continues to provide accurate approximations for systems with constant interactions on two- and three-dimensional lattices or with next-nearest-neighbor interactions, with the results being visually indistinguishable from the numerically exact solution. For systems with disordered interactions, we observe a small but visible degradation of the approximation. To explain this behavior of the free approximation, we develop and apply an asymptotic error analysis scheme to show that the approximation is accurate to the eighth moment in the density of states for systems with constant interactions, but is only accurate to sixth order for systems with disordered interactions. The error analysis also allows us to calculate asymptotic corrections to the density of states, allowing for systematically improvable approximations as well as insight into the sources of error without requiring a direct comparison to an exact solution.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Chemistry
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.88.205113
