CMT Seminar - Sumilan Banerjee (Weizmann Institute of Science) "Solvable model for a dynamical quantum phase transition from fast to slow scrambling"

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December 5, 2016
11:30AM - 12:30PM
Location
4138 Physics Research Building

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Add to Calendar 2016-12-05 11:30:00 2016-12-05 12:30:00 CMT Seminar - Sumilan Banerjee (Weizmann Institute of Science) "Solvable model for a dynamical quantum phase transition from fast to slow scrambling"

Alexei Kitaev has recently given a fascinating new interpretation to a solvable model of interacting fermions, which connects it to thermalization, quantum chaos and information scrambling in quantum black holes. The model, now known as the Sachdev-Ye-Kitaev (or SYK) model, consists of fermions on N-sites with all-to-all quartic interactions. The quantum correlations that diagnose the emergence of quantum chaos can be computed exactly in this model. The result is characteri-zation of quantum chaotic behavior through a scrambling rate, or Lyapunov expo-nent, with a universal value 2πkBT/ћ, which saturates the proven upper bound for the process, as do black holes. The SYK model is now understood as a fixed point representative of a certain class of quantum chaotic or thermal behavior. Here we propose a generalized model that allows to extend this classification. In the gener-alized model we couple N sites forming the SYK model to another set of M sites, coupled to each other only by quadratic (hopping) interactions. In the solvable limit of large N,M we find a quantum phase transition tuned by the finite 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/ћ in the low T limit whereas the Fermi-liquid like phase shows much slower scrambling, proportional to T2.

4138 Physics Research Building Department of Physics physics@osu.edu America/New_York public
Description

Alexei Kitaev has recently given a fascinating new interpretation to a solvable model of interacting fermions, which connects it to thermalization, quantum chaos and information scrambling in quantum black holes. The model, now known as the Sachdev-Ye-Kitaev (or SYK) model, consists of fermions on N-sites with all-to-all quartic interactions. The quantum correlations that diagnose the emergence of quantum chaos can be computed exactly in this model. The result is characteri-zation of quantum chaotic behavior through a scrambling rate, or Lyapunov expo-nent, with a universal value 2πkBT/ћ, which saturates the proven upper bound for the process, as do black holes. The SYK model is now understood as a fixed point representative of a certain class of quantum chaotic or thermal behavior. Here we propose a generalized model that allows to extend this classification. In the gener-alized model we couple N sites forming the SYK model to another set of M sites, coupled to each other only by quadratic (hopping) interactions. In the solvable limit of large N,M we find a quantum phase transition tuned by the finite 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/ћ in the low T limit whereas the Fermi-liquid like phase shows much slower scrambling, proportional to T2.