Out-of-time-order correlations and the fine structure of eigenstate thermalisation

• URL: http://arxiv.org/abs/2103.01161v4
• Date: Fri, 17 Sep 2021 14:31:20 GMT
• Title: Out-of-time-order correlations and the fine structure of eigenstate thermalisation
• Authors: Marlon Brenes, Silvia Pappalardi, Mark T. Mitchison, John Goold and Alessandro Silva
• Abstract summary: 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.
• Score: 58.720142291102135
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Out-of-time-order correlators (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation in interacting quantum many-body systems. It was recently argued that the expected exponential growth of the OTOC is connected to the existence of correlations beyond those encoded in the standard Eigenstate Thermalisation Hypothesis (ETH). We show explicitly, by an extensive numerical analysis of the statistics of operator matrix elements in conjunction with a detailed study of OTOC dynamics, that the OTOC is indeed a precise tool to explore the fine details of the ETH. In particular, while short-time dynamics is dominated by correlations, the long-time saturation behaviour gives clear indications of an operator-dependent energy scale $\omega_{\textrm{GOE}}$ associated to the emergence of an effective Gaussian random matrix theory. We provide an estimation of the finite-size scaling of $\omega_{\textrm{GOE}}$ for the general class of observables composed of sums of local operators in the infinite-temperature regime and found linear behaviour for the models considered.

Related papers

• Spectroscopy and complex-time correlations using minimally entangled typical thermal states [39.58317527488534]
  We introduce a practical approach to computing such correlators using minimally entangled typical thermal states. We show that these numerical techniques capture the finite-temperature dynamics of the Shastry-Sutherland model.
  arXiv  Detail & Related papers  (2024-05-28T18:00:06Z)
• Generalized Free Cumulants for Quantum Chaotic Systems [0.0]
  The eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in isolated quantum systems. We show that the ETH is a sufficient mechanism for thermalization, in general. In particular, we show that reduced density matrices relax to their equilibrium form and that systems obey the Page curve at late times.
  arXiv  Detail & Related papers  (2024-01-24T22:04:41Z)
• Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems [0.0]
  We consider correlations between eigenstates specific to spatially extended systems and that characterise entanglement dynamics and operator spreading. The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalisation hypothesis (ETH) We establish the simplest correlation function that captures these correlations and discuss features of its behaviour that are expected to be universal at long distances and low energies.
  arXiv  Detail & Related papers  (2023-09-22T16:28:15Z)
• Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model [11.353329565587574]
  Quantum scrambling plays an important role in understanding thermalization in closed quantum systems. We show that scrambling is absent for disorder-averaged expectation values of observables. We develop a cumulant expansion approach to approximate the evolution of equal-time observables.
  arXiv  Detail & Related papers  (2022-10-05T17:47:52Z)
• Genuine Multipartite Correlations in a Boundary Time Crystal [56.967919268256786]
  We study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC) We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state.
  arXiv  Detail & Related papers  (2021-12-21T20:25:02Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time [0.0]
  Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. We introduce a novel numerical approach to probe correlations between matrix elements for Hilbert-space dimensions beyond those accessible for exact diagonalization. Considering nonintegrable quantum spin chains, we observe that genuine RMT behavior is absent even for narrow energy windows corresponding to time scales of the order of thermalization time $tau_textth$ of the respective observables.
  arXiv  Detail & Related papers  (2021-10-08T12:21:01Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)
• 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.