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 (OTOCs) 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. OTOCs spread 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.
Highlights
Thermalization in classical many-body systems can be understood from the perspective of dynamical chaos: details of the initial state are effectively forgotten by the exponential divergence of trajectories
Many-body chaos in the self-interacting λφ4 real scalar field theory has been discussed at high temperatures and near its second order thermal phase transition
By employing dimensional reduction we reduced this quantum field theory to a classical statistical field theory and argued why dynamical and chaotic properties may be captured by this approximation
Summary
Thermalization in classical many-body systems can be understood from the perspective of dynamical chaos: details of the initial state are effectively forgotten by the exponential divergence of trajectories. By matching the quantum field theory in the quantum critical regime to the classical field theory via dimensional reduction, we find the Lyapunov exponent to reproduce the linear-in-temperature scaling, that has been found in other strongly coupled theories in accordance with the Maldacena-Shenker-Stanford (MSS) bound [10]. It approaches the non-interacting limit algebraically in a fluctuation parameter and exhibits a cusp at the phase transition. We show that the dynamics of the OTOC offer a qualitatively different perspective on the thermalization dynamics compared to the spectral function
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