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

• Main Authors: Swingle, Brian (Author), Chowdhury, Debanjan (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2018-02-14T18:53:25Z.
• Subjects: Article
• Online Access: Get fulltext

 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[subscript L]. At large N the growth of chaos as measured by λ[subscript L] is slow because the model is weakly interacting, and we find λ[subscript L]≈3.2T/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[subscript B]/c≈1 where c is the Lorentz-invariant speed of particle excitations in the system. We briefly comment on the behavior of λ[subscript L] and v_{B} in the neighboring symmetry broken and unbroken phases.