Onset of many-body chaos in the O(N) model
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PhysRevD.96.065005.pdf
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623.04 KB
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Author(s)
Swingle, Brian
Chowdhury, Debanjan
Date Issued
September 2017
Journal
Physical Review D
Publisher
American Physical Society
Citation
Chowdhury, Debanjan, and Brian Swingle. “Onset of Many-Body Chaos in the O(N) Model.” Physical Review D, vol. 96, no. 6, Sept. 2017. © 2017 American Physical Society
Version
Final published version
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[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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevD.96.065005
