## SciPost Submission Page

# Many-body chaos near a thermal phase transition

### by Alexander Schuckert, Michael Knap

### Submission summary

As Contributors: | Michael Knap · Alexander Schuckert |

Arxiv Link: | https://arxiv.org/abs/1905.00904v1 |

Date submitted: | 2019-05-07 |

Submitted by: | Schuckert, Alexander |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Condensed Matter Physics - Theory |

### Abstract

We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. Chaos spreads ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.