Many-body chaos at weak coupling

By D. Stanford. 2015

172 citations recorded by the source corpus.

A bstractThe strength of chaos in large N quantum systems can be quantified using λL, the rate of growth of certain out-of-time-order four point functions. We calculate λL to leading order in a weakly coupled matrix Φ4 theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e63037ffb252a3bd23c5f23e48bf41e1ce5aaed9

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In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Slow scrambling in disordered quantum systems (2016, background): “Assuming these interaction terms can be resummed [52] at early time to give exponential growth at roughly the inelastic rate , then the interacting early time growth of the anticommutator will be”
Operator Spreading in Random Unitary Circuits (2017, background): “[32] Douglas Stanford, “Many-body chaos at weak coupling,” Journal of High Energy Physics 2016, 9 (2016).”
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].”
On entanglement spreading in chaotic systems (2016, methodology): “This is true in holography and likely to be true in a weakly coupled field theory, using an analysis along the lines of [13].”
Quantum Butterfly Effect in Weakly Interacting Diffusive Metals (2017, methodology): “Since the dynamic interaction (which can be interpreted to be mediated by a dynamically fluctuating boson) rung connects two time folds on opposite sides of the thermal circle, its propagator is given by a bosonic Wightman function [44, 48, 51]”
Random Quantum Circuits (2022, methodology): “The OTOC has been used to diagnose the scrambling of locally-accessible quantum information (165, 166, 167), and its growth in time provides signatures of key properties of quantum many-body systems, including their chaotic (128, 168, 169, 170), disordered (171, 147, 172, 173, 174, 175, 176), or int”
Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, unknown): “For translation-invariant systems they 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].”
Operator growth in the SYK model (2018, methodology): “ t= 1 N e(q 2) t: (2.2) This method of calculation is very similar to the calculation of the OTOC by ladder diagrams, where klabels the number of rungs in the ladder (see [24,27] in the SYK model and [7{9,28,29] in weakly coupled theories). In particular the crucial factors of (q 1) that appear here”
Remarks on the Sachdev-Ye-Kitaev model (2016, background): “This means that at large time, the sum of ladders must satisfy a homogeneous equation that states that adding one rung to each ladder will not change the sum [8, 27].”
Bounding the space of holographic CFTs with chaos (2016, methodology): “A concrete calculation would be to adapt the ladder diagram techniques of [13], where 1/Ñ is the small parameter.”