Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlator

In this talk, I will present our recent work where we investigate many-body quantum chaos in an interacting disordered metal by computing the out-of-time-order correlators (OTOCs). We develop an augmented Keldysh version of Finkel’stein nonlinear sigma model to enable the computation of the regularized and unregularized OTOCs. Both correlators grow exponentially but with different Lyapunov exponents. The result of the regularized exponent is consistent with a previous diagrammatical perturbation study [1], and it obeys the Maldacena-Shenker-Stanford bound [2]. By contrast, the unregularized exponent exceeds the bound which was proved for the regularized OTOC. Unlike the regularized exponent which originates entirely from the inelastic collisions between particles, the unregularized exponent contains an extra contribution from virtual processes unrelated to many-body quantum chao, i.e., the elastic scattering of electrons off the Friedel oscillations of the charge density. We therefore argue that the unregularized exponent is not a reliable measure for many-body quantum chaos.

 

[1] A. A. Patel, D. Chowdhury, S. Sachdev, and B. Swingle, Phys. Rev. X 7, 031047 (2017).

[2] J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 106.

 

[3] Y. Liao and V. Galitski, Phys. Rev. B 98, 205124 (2018).

 

Lunch is at 12:00 pm; the talk begins at 12:15pm.