Densities of states for disordered systems from free probability
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...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/88941 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0001-7111-0176 |
| _version_ | 1826206621122953216 |
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| author | Chen, Jiahao Van Voorhis, Troy Welborn, Matthew Gregory |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Chen, Jiahao Van Voorhis, Troy Welborn, Matthew Gregory |
| author_sort | Chen, Jiahao |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:35:47Z |
| format | Article |
| id | mit-1721.1/88941 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:35:47Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/889412022-10-01T15:55:26Z Densities of states for disordered systems from free probability Chen, Jiahao Van Voorhis, Troy Welborn, Matthew Gregory Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Chemistry Welborn, Matthew Gregory Chen, Jiahao Van Voorhis, Troy 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. National Science Foundation (U.S.) (SOLAR Grant 1035400) National Science Foundation (U.S.). Graduate Research Fellowship 2014-08-21T14:10:51Z 2014-08-21T14:10:51Z 2013-11 2013-08 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/88941 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 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0001-7111-0176 en_US http://dx.doi.org/10.1103/PhysRevB.88.205113 Physical Review B 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 American Physical Society |
| spellingShingle | Chen, Jiahao Van Voorhis, Troy Welborn, Matthew Gregory Densities of states for disordered systems from free probability |
| title | Densities of states for disordered systems from free probability |
| title_full | Densities of states for disordered systems from free probability |
| title_fullStr | Densities of states for disordered systems from free probability |
| title_full_unstemmed | Densities of states for disordered systems from free probability |
| title_short | Densities of states for disordered systems from free probability |
| title_sort | densities of states for disordered systems from free probability |
| url | http://hdl.handle.net/1721.1/88941 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0001-7111-0176 |
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