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Quantum chaos in many-body systems may be characterized by the Lyapunovexponent defined as the exponential growth rate of out-of-time-ordercorrelators (OTOC). So far Lyaponov exponents around various quantum criticalpoints (QCP) remain largely unexplored. Here, we investigate the Lyapunovexponent around QCPs of the Gross-Neveu (GN) model with $N$ flavors of Diracfermions in (2+1) dimensions. Around the GN quantum phase transition between aDirac semimetal and a gapped insulator breaking $Z_2$ symmetry (e.g., inversionsymmetry of the honeycomb lattice), we find that the Lyaponov exponent$\lambda_L \approx 3.5 T/N$ at temperature $T$ and to the leading order of$1/N$ in the large-$N$ expansion. We also obtain the quantum scattering rate ofan excitation with energy $\epsilon$, which is proportional to $\sqrt{\epsilonT}/N$ at low energy. We further discuss possible experimental relevances of theGN model in many-body systems.

Universal properties of many-body quantum chaos at Gross-Neveu criticality