Slow scrambling in disordered quantum systems
By Brian Swingle, D. Chowdhury. 2016
205 citations recorded by the source corpus.
Recent work has studied the growth of commutators as a probe of chaos and information scrambling in quantum many-body systems. In this work we study the effect of static disorder on the growth of commutators in a variety of contexts. We find generically that disorder slows the onset of scrambling, and, in the case of a many-body localized state, partially halts it. We access the many-body localized state using a standard fixed point Hamiltonian, and we show that operators exhibit slow logarithmic growth under time evolution. We compare the result with the expected growth of commutators in both localized and delocalized non-interacting disordered models. Finally, based on a scaling argument, we state a conjecture about the effect of weak interactions on the growth of commutators in an interacting diffusive metal.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/082be13ea74a6c598f259cd74328c1337630257d
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- A quantum hydrodynamical description for scrambling and many-body chaos (2017, background): “For instance in [22, 23] chaos is described by a diffusive spreading around the exponential growth2”
- 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”
- Onset of many-body chaos in the $O(N)$ model (2017, background): “Recent work has also focused on the possible relation between diffusion, the chaos exponent, and the butterfly velocity [27,67,62].”
- Locality, Quantum Fluctuations, and Scrambling (2018, background): “assuming there is a well-defined butterfly velocity vB (a different ansatz is needed for localized systems [40–43]), furthered studied by [44].”
- Quantum Butterfly Effect in Weakly Interacting Diffusive Metals (2017, background): “On general scaling grounds, the butterfly velocity can be estimated to be vB ∼ √ Dγin, where D ∼ l2τ−1 is the diffusion constant (l ≡ mean-free path, τ−1 ≈ elastic scattering rate) and γin is a small interaction-induced inelastic scattering rate [23].”
- 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 Cðt; rÞ [139,147].”
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves (2016, background): “r y eect is provided by the out-of-time-order correlator (OTOC) that was rst introduced by Larkin and Ovchinnokov[2], revived by Kitaev [3, 4] and extensively discussed by a number of works recently [5, 6, 7, 8]. OTOC is dened by A(t) = D O(t)O~(0)O(t)O~(0) E ; (1) where O(t) and O~(t) are two local”
- Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator (2016, background): “[14] Brian Swingle and Debanjan Chowdhury, “Slow scrambling in disordered quantum systems,” Phys.”
- Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models (2016, background): “[33, 34] for other discussions on diffusion and butterfly effect in solid state systems.”