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 publicAlexei 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.
