Time-evolution of local information: thermalization dynamics of local observables

• URL: http://arxiv.org/abs/2105.11206v4
• Date: Wed, 17 Aug 2022 13:22:23 GMT
• Title: Time-evolution of local information: thermalization dynamics of local observables
• Authors: Thomas Klein Kvorning, Lo\"ic Herviou, and Jens H. Bardarson
• Abstract summary: Quantum many-body dynamics results in increasing entanglement that eventually leads to thermalization of local observables. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. We first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well defined locally conserved von Neumann information current.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Quantum many-body dynamics generically results in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such decoupling of local degrees of freedom for the mixed field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we can motivate algorithms based on the intuition that information for statistical reasons flow from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.

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)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators [0.0]
  We introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems.
  arXiv  Detail & Related papers  (2024-08-15T19:00:24Z)
• Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution [0.0]
  We use the recently introduced information lattice to organize quantum information into different scales. We define local information and information currents which we employ to systematically discard long-range quantum correlations. We present results for energy transport in the mixed-field Ising model and magnetization transport in an open XX spin chain.
  arXiv  Detail & Related papers  (2023-10-09T18:00:07Z)
• Deep learning delay coordinate dynamics for chaotic attractors from partial observable data [0.0]
  We utilize deep artificial neural networks to learn discrete discrete time maps and continuous time flows of the partial state. We demonstrate the capacity of deep ANNs to predict chaotic behavior from a scalar observation on a manifold of dimension three via the Lorenz system.
  arXiv  Detail & Related papers  (2022-11-20T19:25:02Z)
• Scalably learning quantum many-body Hamiltonians from dynamical data [1.702884126441962]
  We introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins.
  arXiv  Detail & Related papers  (2022-09-28T18:00:57Z)
• Spreading of a local excitation in a Quantum Hierarchical Model [62.997667081978825]
  We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. A localization mechanism is found and the excitation remains close to its initial position at arbitrary times.
  arXiv  Detail & Related papers  (2022-07-14T10:05:20Z)
• From locality to irregularity: Introducing local quenches in massive scalar field theory [68.8204255655161]
  We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension. We identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables.
  arXiv  Detail & Related papers  (2022-05-24T18:00:07Z)
• 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)
• Information-Theoretic Memory Scaling in the Many-Body Localization Transition [68.8204255655161]
  We study the understanding of local memory in the context of many-body localization. We introduce the dynamical Holevo quantity as the true quantifier of local memory. We find clear scaling behavior in its steady-state across the many-body localization transition.
  arXiv  Detail & Related papers  (2020-09-09T18:00:01Z)
• CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations [72.4716073597902]
  We propose a method to learn object Canonical Point Cloud Representations of dynamically or moving objects. We demonstrate the effectiveness of our method on several applications including shape reconstruction, camera pose estimation, continuoustemporal sequence reconstruction, and correspondence estimation.
  arXiv  Detail & Related papers  (2020-08-06T17:58:48Z)

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.