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Condensed Matter > Strongly Correlated Electrons

arXiv:1805.12299 (cond-mat)
[Submitted on 31 May 2018]

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

Authors:Shao-Kai Jian, Hong Yao
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Abstract: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 $\lambda_L \approx 3.5 T/N$ at temperature $T$ and to the leading order of $1/N$ in the large-$N$ expansion. We also obtain the quantum scattering rate of an excitation with energy $\epsilon$, which is proportional to $\sqrt{\epsilon T}/N$ at low energy. We further discuss possible experimental relevances of the GN model in many-body systems.
Comments: 7 pages, 7 figures + appendix
Subjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1805.12299 [cond-mat.str-el]
  (or arXiv:1805.12299v1 [cond-mat.str-el] for this version)
  https://doi.org/10.48550/arXiv.1805.12299

Submission history

From: Shaokai Jian [view email]
[v1] Thu, 31 May 2018 02:58:39 UTC (325 KB)
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