Higher-order correlator families are recast as operator-space geometries that, when conditioned on a chosen subspace, reveal irreducible structures distinguishing free, integrable, chaotic, localized, and Floquet dynamics.
Fritzsch and P.W
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multi-time correlation functions. We consider the dynamics of higher-order out-of-time-order correlators (OTOCs) in a minimal circuit model for quantum dynamics. This model mimics the dynamics of a structured subsystem locally coupled to a maximally random environment. We prove the exponential decay of all higher-order OTOCs and fully characterize the relevant time scales, showing how local operators approach free independence at late times. We show that the effects of the environment on the local subsystem can be captured in a higher-order influence matrix, which allows for a Markovian description of the dynamics provided an auxiliary degree of freedom is introduced. This degree of freedom directly yields a dynamical picture for the OTOCs in terms of free cumulants from free probability, consistent with recent predictions from the full eigenstate thermalization hypothesis (ETH). This approach and the relevant influence matrix are expected to be applicable in more general settings and present a first step to characterizing quantum memory in higher-order OTOCs.
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citing papers explorer
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Irreducible Geometry of Higher-Order Correlator Families
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Page Curve for Local-Operator Entanglement from Free Probability
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Timescales for Deep and Full Thermalization
In a chaotic quantum system, higher-order correlations reach thermal equilibrium faster than state design moments, both relaxing exponentially.
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Quantum many-body scars in random unitary circuits
A constructed random unitary circuit hosts one scar whose perturbations thermalize via fluctuating interfaces while the scar imprints a non-local transition in entanglement dynamics.
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Complexity of Quadratic Quantum Chaos
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
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Lecture Notes on Replica Tensor Networks for Random Quantum Circuits
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.