Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems
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Edelman-2012-Error Analysis of Free Probability.pdf
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Author(s)
Chen, Jiahao
Hontz, Eric Richard
Moix, Jeremy
Van Voorhis, Troy
Welborn, Matthew Gregory
Suárez, Alberto
Movassagh, Ramis
Edelman, Alan
Date Issued
July 2012
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Chen, Jiahao et al. “Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems.” Physical Review Letters 109.3 (2012): 036403. © 2012 American Physical Society.
Version
Final published version
Abstract
Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble-averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with perturbation theory and isotropic entanglement theory.
MIT Department
Massachusetts Institute of Technology. Department of Chemistry
Massachusetts Institute of Technology. Department of Mathematics
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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/PhysRevLett.109.036403
