Random Interactions

Solvable model for a dynamical quantum phase transition from fast to slow scrambling

by Prof. Sumilan Bannerjee (Indian Institute of Science, Bangalore)

Friday, May 26, 2017 from to (Asia/Kolkata)
at A304
Description
Alexei Kitaev has recently given a new interpretation to a solvable model of interacting fermions, now known as Sachdve-Ye-Kitaev (SYK) model, connecting it to thermalization, quantum chaos and information scrambling in black holes. The correlations that diagnose quantum chaos has been computed in this model leading to a scrambling rate with a universal value 2πkBT/ℏ at temperature T. The SYK model is now understood as a fixed point for a certain class of quantum chaotic behavior. We propose a generalized model that extends this classification. In the generalized model, we couple N sites forming the SYK model to another set of M sites, connected to each other only via quadratic coupling. In the solvable limit of large N,M we find a quantum phase transition tuned by the ratio p=M/N from a non Fermi liquid SYK like phase to a Fermi liquid. We show that the entire SYK-like phase shows scrambling at the universal rate 2πkBT/ℏ at low temperature whereas the Fermi-liquid like phase shows much slower scrambling, proportional to T2.