Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems
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...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/72145 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0002-6547-3402 https://orcid.org/0000-0001-7676-3133 https://orcid.org/0000-0002-4078-6752 https://orcid.org/0000-0001-7111-0176 |
| _version_ | 1826253197761576960 |
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| author | Chen, Jiahao Hontz, Eric Richard Moix, Jeremy Van Voorhis, Troy Welborn, Matthew Gregory Suárez, Alberto Movassagh, Ramis Edelman, Alan |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Chen, Jiahao Hontz, Eric Richard Moix, Jeremy Van Voorhis, Troy Welborn, Matthew Gregory Suárez, Alberto Movassagh, Ramis Edelman, Alan |
| author_sort | Chen, Jiahao |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:37:55Z |
| format | Article |
| id | mit-1721.1/72145 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:37:55Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/721452022-09-29T20:27:44Z Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems Chen, Jiahao Hontz, Eric Richard Moix, Jeremy Van Voorhis, Troy Welborn, Matthew Gregory Suárez, Alberto Movassagh, Ramis Edelman, Alan Massachusetts Institute of Technology. Department of Chemistry Massachusetts Institute of Technology. Department of Mathematics Edelman, Alan Chen, Jiahao Hontz, Eric Richard Moix, Jeremy Van Voorhis, Troy Welborn, Matthew Gregory Movassagh, Ramis Edelman, Alan 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. National Science Foundation (U.S.). Division of Chemistry (grant no. 1112825) National Science Foundation (U.S.) (SOLAR grant no. 1035400) United States. Defense Advanced Research Projects Agency (grant no. N99001-10-1-4063) National Science Foundation (U.S.) (DMS grant no. 1016125) 2012-08-15T15:58:27Z 2012-08-15T15:58:27Z 2012-07 2012-02 Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/72145 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. https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0002-6547-3402 https://orcid.org/0000-0001-7676-3133 https://orcid.org/0000-0002-4078-6752 https://orcid.org/0000-0001-7111-0176 en_US http://dx.doi.org/10.1103/PhysRevLett.109.036403 Physical Review Letters 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. application/pdf American Physical Society APS |
| spellingShingle | Chen, Jiahao Hontz, Eric Richard Moix, Jeremy Van Voorhis, Troy Welborn, Matthew Gregory Suárez, Alberto Movassagh, Ramis Edelman, Alan Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems |
| title | Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems |
| title_full | Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems |
| title_fullStr | Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems |
| title_full_unstemmed | Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems |
| title_short | Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems |
| title_sort | error analysis of free probability approximations to the density of states of disordered systems |
| url | http://hdl.handle.net/1721.1/72145 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0002-6547-3402 https://orcid.org/0000-0001-7676-3133 https://orcid.org/0000-0002-4078-6752 https://orcid.org/0000-0001-7111-0176 |
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