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 $z > 1$.
Highlights
Elucidating the physics of thermalization in isolated quantum systems [1,2,3,4] represents an ongoing challenge in quantum many-body physics, and great progress has been made in recent years because of advances in both theory and experiments [5,6,7,8,9,10,11,12]
We probe scrambling at length scales x much larger than the mean-free path l and the screening length K−2 1 but smaller than the eventual localization [59] length lekFl of the electron wave functions [30]. [The light-cone-like growth of fðt; xÞ will be arrested beyond this localization length; i.e., the operator-radius RðtÞ is bounded by this length.] the same approximations and lines of reasoning we used in three dimensions work in two dimensions, and the Lyapunov exponent is still given by
We have studied the spread of many-body quantum chaos due to electron-electron interactions in diffusive metals
Summary
Elucidating the physics of thermalization in isolated quantum systems [1,2,3,4] represents an ongoing challenge in quantum many-body physics, and great progress has been made in recent years because of advances in both theory and experiments [5,6,7,8,9,10,11,12]. We find that chaos grows in a ballistic fashion, with a velocity that is parametrically smaller than the Fermi velocity at low temperatures These computations confirm a recent argument by two of us [23] that even though the transport of charge and energy is diffusive in such metals, generic operators grow ballistically The rest of this paper is organized as follows: In Sec. II, we define our model of interacting electrons in the presence of static disorder and set up the basic elements required for carrying out perturbation theory to leading order in the coupling strength. Ħ 1⁄4 kB 1⁄4 1 in the rest of this paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
