Onset of many-body chaos in the $O(N)$ model

Debanjan Chowdhury; Brian Swingle

doi:10.1103/PhysRevD.96.065005

paper

Onset of many-body chaos in the $O (N)$ model

arXiv:1703.02545 · doi:10.1103/PhysRevD.96.065005

Abstract

The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with $N$ components in the $(2 + 1)$ -dimensional $O (N)$ nonlinear sigma model to leading order in $1/ N$ . The system is taken to be in thermal equilibrium at a temperature $T$ above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted $λ_{L}$ . At large $N$ the growth of chaos as measured by $λ_{L}$ is slow because the model is weakly interacting, and we find $λ_{L} \approx 3.2 T / N$ . The scaling with temperature is dictated by conformal invariance of the underlying quantum critical point. We also show that operators grow ballistically in space with a "butterfly velocity" given by $v_{B} / c \approx 1$ where $c$ is the Lorentz-invariant speed of particle excitations in the system. We briefly comment on the behavior of $λ_{L}$ and $v_{B}$ in the neighboring symmetry broken and unbroken phases.

(1+55) pages, 13 figures; (v2) Final published version

Onset of many-body chaos in the $O (N)$ model

Abstract

References in corpus (13)

Cited by in corpus (102)

Onset of many-body chaos in the O(N) model

Abstract

References in corpus (13)

Cited by in corpus (102)

Onset of many-body chaos in the $O (N)$ model