4.7 Article

Quantum Butterfly Effect in Weakly Interacting Diffusive Metals

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PHYSICAL REVIEW X
卷 7, 期 3, 页码 -

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AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.7.031047

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资金

  1. National Science Foundation (NSF) [DMR-1360789]
  2. Multidisciplinary University Research Initiative (MURI) from Army Research Office (ARO) [W911NF-14-1-0003]
  3. Simons Foundation as part of the It From Qubit Collaboration
  4. Simons Investigator grant
  5. Gordon and Betty Moore Foundation under Emergent Phenomena in Quantum Systems (EPiQS) initiative, at MIT [GBMF-4303]
  6. Government of Canada through Industry Canada
  7. Province of Ontario through Ministry of Research and Innovation
  8. Cenovus Energy at the Perimeter Institute
  9. Direct For Mathematical & Physical Scien
  10. Division Of Materials Research [1360789] Funding Source: National Science Foundation

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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.

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