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

By D. Chowdhury, Brian Swingle. 2017

134 citations recorded by the source corpus.

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 $\lambda_L$. At large $N$ the growth of chaos as measured by $\lambda_L$ is slow because the model is weakly interacting, and we find $\lambda_L \approx 3.2 T/N$. 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 $\lambda_L$ and $v_B$ in the neighboring symmetry broken and unbroken phases.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6ffe7f46cc00ef870884a6741878a3ed698ca249

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. V. Khemani
3. Brian Swingle
4. Shenglong Xu
5. D. Huse
6. S. Vijay
7. Matthew Fisher
8. Frank Pollmann

In Statistical and Nonlinear Physics

1. A. Nahum
2. Shenglong Xu
3. Brian Swingle
4. V. Khemani
5. S. Sachdev
6. S. Vijay
7. D. Huse
8. D. Chowdhury

Citations in the corpus

• Operator Spreading in Random Unitary Circuits (2017, background): “scaling forms extend to nonintegrable models with timeindependent Hamiltonians, although we note that a previous calculation in a different setting has instead found a front that does not broaden with time, and is governed by a traveling wave equation [31] (see also [37, 38]).”
• Locality, Quantum Fluctuations, and Scrambling (2018, background): “[28] D.”
• Translationally Invariant Non-Fermi-Liquid Metals with Critical Fermi Surfaces: Solvable Models (2018, background): “Other models display a different form for the spatial structure of C(t, r) [109, 117].”
• Quantum Butterfly Effect in Weakly Interacting Diffusive Metals (2017, background): “Computing f(t,x) involves defining the action on a complex-time contour with real time folds separated by iβ/2 [44, 48, 50, 51].”
• Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “theories[23, 31, 33] and (iii) weakly interacting disordered systems whose low-temperature dynamics are described, to leading order, via a semiclassical weak scattering theory of quasiparticles[32].”
• Emergent statistical mechanics of entanglement in random unitary circuits (2018, unknown): “[37] Debanjan Chowdhury and Brian Swingle.”
• Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, background): “have been studied in weakly coupled [42] local quantum field theories [15, 16, 18, 43, 44], in models for black hole scrambling [12, 28, 45] and more recently in local random circuits [25, 26].”