2018/05/31 by Jian, Shao-Kai, Yao, Hong
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.1805.12299
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 Z2 symmetry (e.g., inversion symmetry of the honeycomb lattice), we find that the Lyaponov exponent λL ≈ 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 √(εT)/N at low energy. We further discuss possible experimental relevances of the GN model in many-body systems.