Quantum Butterfly Effect in Weakly Interacting Diffusive Metals
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PhysRevX.7.031047.pdf
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577.68 KB
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Author(s)
Patel, Aavishkar A.
Sachdev, Subir
Chowdhury, Debanjan
Swingle, Brian Gordon
Date Issued
September 2017
Journal
Physical Review X
Publisher
American Physical Society
Citation
Patel, Aavishkar A. et al. "Quantum Butterfly Effect in Weakly Interacting Diffusive Metals." Physical Review X 7, 3 (September 2017): 031047
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1103/PhysRevX.7.031047
