Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling

• URL: http://arxiv.org/abs/2509.08060v1
• Date: Tue, 09 Sep 2025 18:01:45 GMT
• Title: Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling
• Authors: Felix Fritzsch, Gabriel O. Alves, Michael A. Rampp, Pieter W. Claeys,
• Abstract summary: We introduce a solvable many-body quantum model, which we term boundary scrambling, for which the full dynamics of higher-order OTOCs is analytically tractable.<n>We obtain exact expressions for (higher-order) correlations between matrix elements and show these to be stable away from the solvable point.<n>These results provide insight into the emergence of random-matrix behavior from structured Floquet dynamics and show how techniques from free probability can be applied in the construction of exactly-solvable many-body models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Out-of-time-order correlation functions (OTOCs) and their higher-order generalizations present important probes of quantum information dynamics and scrambling. We introduce a solvable many-body quantum model, which we term boundary scrambling, for which the full dynamics of higher-order OTOCs is analytically tractable. These dynamics support a decomposition into free cumulants and unify recent extensions of the eigenstate thermalization hypothesis with predictions from random quantum circuit models. We obtain exact expressions for (higher-order) correlations between matrix elements and show these to be stable away from the solvable point. The solvability is enabled by the identification of a higher-order Markovian influence matrix, capturing the effect of the full system on a local subsystem. These results provide insight into the emergence of random-matrix behavior from structured Floquet dynamics and show how techniques from free probability can be applied in the construction of exactly-solvable many-body models.

Related papers

• Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits [72.0643009153473]
  We show that expressive variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size.<n>As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions.<n>We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class.
  arXiv  Detail & Related papers  (2026-01-05T08:04:33Z)
• Complexity of Quadratic Quantum Chaos [1.3707825707652799]
  We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices.<n>Unlike integrable two-body fermionic systems, the corresponding hard-core boson models exhibit genuinely chaotic dynamics.<n>These minimal models may constitute promising and resource-efficient candidates for probing quantum chaos and information scrambling on near-term quantum devices.
  arXiv  Detail & Related papers  (2025-09-04T10:09:46Z)
• Free Independence and Unitary Design from Random Matrix Product Unitaries [0.0]
  We study the emergence of freeness in a random matrix unitary ensemble.<n>With only bond dimension, these unitaries reproduce Haar values of higher-order OTOCs for local, finite-trace observables.<n>Our results highlight the need to refine previous notions of unitary design in the context of operator dynamics.
  arXiv  Detail & Related papers  (2025-07-31T18:00:00Z)
• Free Probability in a Minimal Quantum Circuit Model [0.0]
  We study the dynamics of higher-order out-of-time-order correlators (OTOCs) in a minimal circuit model for quantum dynamics.<n>We prove the exponential decay of all higher-order OTOCs and fully characterize the relevant time scales.<n>This approach and the relevant influence matrix are expected to be applicable in more general settings.
  arXiv  Detail & Related papers  (2025-06-12T18:00:11Z)
• Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility [5.866320821393424]
  We use quantum fidelity susceptibility to precisely identify the mobility edges in generalized Aubry-Andr'e models. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality.
  arXiv  Detail & Related papers  (2024-05-22T01:33:04Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [44.99833362998488]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient.<n>We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics.<n>We establish that scaling predictions are matched by a privileged process and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all time scales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems [0.0]
  Eigenstate-Thermalization-Hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics. We show that the dynamics of four-time correlation functions are encoded in fourth-order free cumulants, as predicted by ETH.
  arXiv  Detail & Related papers  (2023-03-01T18:18:51Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.