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Alexei Kitaev has recently given a new interpretation to a zero-dimensional solvable
model of interacting fermions, now known as Sachdve-Ye-Kitaev (SYK) model,
connecting it to non-Fermi liquid metals, thermalization and many-body quantum chaos
or information scrambling. The correlations that diagnose many-body quantum chaos
has been computed in this model leading to a Lyapunov exponent or scrambling rate
with a universal value 2πkBT/ћ which only depends on temperature T. The SYK model
is now understood as a fixed point for a certain class of quantum chaotic behavior.
Following this, there have been a lot of activities to characterize thermalization
dynamics and quantum phases and phase transitions via many-body quantum chaos.
After a brief introduction to the subject, I will discuss two models, related to SYK
model, one in zero and other in higher dimensions, which exhibit dynamical transitions
between distinct chaotic fixed points, namely from fast scrambling non-Fermi liquid
phases with linear-T scrambling rate to Fermi liquid-like phase with much slower
scrambling rate, e.g., proportional to T2. |