From ETH to algebraic relaxation of OTOCs in systems with conserved quantities

• URL: http://arxiv.org/abs/2106.00234v2
• Date: Mon, 21 Jun 2021 10:50:24 GMT
• Title: From ETH to algebraic relaxation of OTOCs in systems with conserved quantities
• Authors: Vinitha Balachandran, Giuliano Benenti, Giulio Casati, and Dario Poletti
• Abstract summary: We show that the presence of local conserved quantities typically results in, at the fastest, an algebraic relaxation of the OTOC. Our result relies on the algebraic scaling of the infinite-time value of OTOCs with system size. We show that time-independence of the Hamiltonian is not necessary as the above conditions can occur in time-dependent systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a mean to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the fastest, an algebraic relaxation of the OTOC provided (i) the dynamics is local and (ii) the system follows the eigenstate thermalization hypothesis. Our result relies on the algebraic scaling of the infinite-time value of OTOCs with system size, which is typical in thermalizing systems with local conserved quantities, and on the existence of finite speed of propagation of correlations for finite-range-interaction systems. We show that time-independence of the Hamiltonian is not necessary as the above conditions (i) and (ii) can occur in time-dependent systems, both periodic or aperiodic. We also remark that our result can be extended to systems with power-law interactions.

Related papers

• Thermalization Dynamics in Closed Quantum Many Body Systems: a Precision Large Scale Exact Diagonalization Study [0.0]
  We study the finite-size deviation between the resulting equilibrium state and the thermal state. We find that the deviations are well described by the eigenstate thermalization hypothesis. We also find that local observables relax towards equilibrium exponentially with a relaxation time scale that grows linearly with system length.
  arXiv  Detail & Related papers  (2024-09-27T15:58:05Z)
• Exploring Hilbert-Space Fragmentation on a Superconducting Processor [23.39066473461786]
  Isolated interacting quantum systems generally thermalize, yet there are several counterexamples for the breakdown of ergodicity. Recently, ergodicity breaking has been observed in systems subjected to linear potentials, termed Stark many-body localization. Here, we experimentally explore initial-state dependent dynamics using a ladder-type superconducting processor with up to 24 qubits.
  arXiv  Detail & Related papers  (2024-03-14T04:39:14Z)
• Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations [31.223649540164928]
  We propose an alternative formalism that turns any non-autonomous unitary dynamical system into an autonomous unitary system. This makes the simulation with time-dependent Hamiltonians not much more difficult than that of time-independent Hamiltonians. We show how our new quantum protocol for time-dependent Hamiltonians can be performed in a resource-efficient way and without measurements.
  arXiv  Detail & Related papers  (2023-12-05T14:59:23Z)
• Temporal fluctuations of correlators in integrable and chaotic quantum systems [0.0]
  We provide bounds on temporal fluctuations around the infinite-time average of out-of-time-ordered and time-ordered correlators of many-body quantum systems without energy gap degeneracies. For physical initial states, our bounds predict the exponential decay of the temporal fluctuations as a function of the system size.
  arXiv  Detail & Related papers  (2023-07-17T12:35:38Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• 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)
• 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)
• Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions [0.0]
  A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has so far mostly been observed in systems with a high-dimensional local Hilbert space. We show that a parametrically long period of exponential growth requires the butterfly velocity to be much larger than the Lyapunov exponent times a microscopic length scale.
  arXiv  Detail & Related papers  (2020-09-21T18:02:22Z)
• Quantum relaxation in a system of harmonic oscillators with time-dependent coupling [0.0]
  We analyze the relaxation of nonequilibrium initial distributions for a system of coupled one-dimensional harmonic oscillators. We show that in general the system studied here tends to equilibrium, but the relaxation can be retarded depending on the values of the parameters.
  arXiv  Detail & Related papers  (2020-07-06T12:57:18Z)

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.