Quantum Butterfly Effect in Weakly Interacting Diffusive Metals

By Aavishkar A. Patel, D. Chowdhury, S. Sachdev, Brian Swingle. 2017

147 citations recorded by the source corpus.

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 $z > 1$.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/91f6ecc0cc0df90b6dd84ebac47493e1a3cdf466

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. V. Khemani
3. Shenglong Xu
4. Brian Swingle
5. D. Huse
6. S. Vijay
7. Matthew Fisher
8. Frank Pollmann

In Condensed Matter Physics

1. V. Khemani
2. A. Nahum
3. Shenglong Xu
4. D. Huse
5. Brian Swingle
6. S. Vijay
7. Frank Pollmann
8. Tibor Rakovszky

Citations in the corpus

• Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “theories[23, 31, 33] and (iii) weakly interacting disordered systems whose low-temperature dynamics are described, to leading order, via a semiclassical weak scattering theory of quasiparticles[32].”
• Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, unknown): “For translation-invariant systems they have been studied in weakly coupled [42] local quantum field theories [15,16,18,43,44], in models for black hole scrambling [12,28,45], and more recently in local random circuits [25,26].”
• Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws (2017, background): “[35,58]), although, to our knowledge, this is the first study of this dependence in infinite-temperature ergodic systems.”
• Locality, Quantum Fluctuations, and Scrambling (2018, background): “, purely exponential growth of C(r, t), plus the ballistic growth of the OTOC, implies that the wavefront is sharp, and sharp wavefronts have been identified in a broad class of holographic/large N models, including the O(N) model [28], the diffusive metal [29] and the coupled SYK model [30–32].”
• Operator Spreading in Random Unitary Circuits (2017, background): “This picture differs from that obtained in a number of previous calculations using many-body perturbation theory [31,33,37,38], and it will be interesting to understand the reasons for these differences.”