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

arXiv:1805.12299May 31, 201810 citations

N

flavors of Dirac fermions in (2+1) dimensions. Around the GN quantum phase transition between a Dirac semimetal and a gapped insulator breaking

Z_2

symmetry (e.g., inversion symmetry of the honeycomb lattice), we find that the Lyaponov exponent

λ_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 of an excitation with energy

ε

, which is proportional to

\sqrt{εT}/N

at low energy. We further discuss possible experimental relevances of the GN model in many-body systems.