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

Understand

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 $\lambda_L$.