Quantum Butterfly Effect in Weakly Interacting Diffusive Metals
We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic f...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114255 |
| _version_ | 1826210714283409408 |
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| author | Patel, Aavishkar A. Sachdev, Subir Chowdhury, Debanjan Swingle, Brian Gordon |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Patel, Aavishkar A. Sachdev, Subir Chowdhury, Debanjan Swingle, Brian Gordon |
| author_sort | Patel, Aavishkar A. |
| collection | MIT |
| description | We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron-field operators inherits a light-cone-like growth, arising from an interplay of a growth (Lyapunov) exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder. In two spatial dimensions, the Lyapunov exponent is universally related at weak coupling to the sheet resistivity. We are able to define an effective temperature-dependent butterfly velocity, a speed limit for the propagation of quantum information that is much slower than microscopic velocities such as the Fermi velocity and that is qualitatively similar to that of a quantum critical system with a dynamical critical exponent z > 1. |
| first_indexed | 2024-09-23T14:54:00Z |
| format | Article |
| id | mit-1721.1/114255 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T14:54:00Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1142552022-10-01T23:16:03Z Quantum Butterfly Effect in Weakly Interacting Diffusive Metals Patel, Aavishkar A. Sachdev, Subir Chowdhury, Debanjan Swingle, Brian Gordon Massachusetts Institute of Technology. Department of Physics Chowdhury, Debanjan Swingle, Brian Gordon We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron-field operators inherits a light-cone-like growth, arising from an interplay of a growth (Lyapunov) exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder. In two spatial dimensions, the Lyapunov exponent is universally related at weak coupling to the sheet resistivity. We are able to define an effective temperature-dependent butterfly velocity, a speed limit for the propagation of quantum information that is much slower than microscopic velocities such as the Fermi velocity and that is qualitatively similar to that of a quantum critical system with a dynamical critical exponent z > 1. United States. Army Research Office (Grant W911NF-14-1-0003) 2018-03-21T19:10:00Z 2018-03-21T19:10:00Z 2017-09 2017-05 2018-03-02T14:33:50Z Article http://purl.org/eprint/type/JournalArticle 2160-3308 http://hdl.handle.net/1721.1/114255 Patel, Aavishkar A. et al. “Quantum Butterfly Effect in Weakly Interacting Diffusive Metals.” Physical Review X 7, 3 (September 2017): 031047 © The Author(s) http://dx.doi.org/10.1103/PhysRevX.7.031047 Physical Review X Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/ application/pdf American Physical Society Physical Review X |
| spellingShingle | Patel, Aavishkar A. Sachdev, Subir Chowdhury, Debanjan Swingle, Brian Gordon Quantum Butterfly Effect in Weakly Interacting Diffusive Metals |
| title | Quantum Butterfly Effect in Weakly Interacting Diffusive Metals |
| title_full | Quantum Butterfly Effect in Weakly Interacting Diffusive Metals |
| title_fullStr | Quantum Butterfly Effect in Weakly Interacting Diffusive Metals |
| title_full_unstemmed | Quantum Butterfly Effect in Weakly Interacting Diffusive Metals |
| title_short | Quantum Butterfly Effect in Weakly Interacting Diffusive Metals |
| title_sort | quantum butterfly effect in weakly interacting diffusive metals |
| url | http://hdl.handle.net/1721.1/114255 |
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