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@ARTICLE{Heitmann:916119,
      author       = {Heitmann, Tjark and Richter, Jonas and Jin, Fengping and
                      Michielsen, Kristel and De Raedt, Hans and Steinigeweg,
                      Robin},
      title        = {{S}patiotemporal dynamics of classical and quantum density
                      profiles in low-dimensional spin systems},
      journal      = {Physical review research},
      volume       = {4},
      number       = {4},
      issn         = {2643-1564},
      address      = {College Park, MD},
      publisher    = {APS},
      reportid     = {FZJ-2022-05950},
      pages        = {043147},
      year         = {2022},
      abstract     = {We provide a detailed comparison between the dynamics of
                      high-temperature spatiotemporal correlation functions in
                      quantum and classical spin models. In the quantum case, our
                      large-scale numerics are based on the concept of quantum
                      typicality, which exploits the fact that random pure quantum
                      states can faithfully approximate ensemble averages,
                      allowing the simulation of spin-1/2 systems with up to 40
                      lattice sites. Due to the exponentially growing Hilbert
                      space, we find that for such system sizes even a single
                      random state is sufficient to yield results with extremely
                      low noise that is negligible for most practical purposes. In
                      contrast, a classical analog of typicality is missing. In
                      particular, we demonstrate that to obtain data with a
                      similar level of noise in the classical case, extensive
                      averaging over classical trajectories is required, no matter
                      how large the system size. Focusing on
                      (quasi-)one-dimensional spin chains and ladders, we find
                      remarkably good agreement between quantum and classical
                      dynamics. This applies not only to cases where both the
                      quantum and classical models are nonintegrable but also to
                      cases where the quantum spin-1/2 model is integrable and the
                      corresponding classical s → ∞ model is not. Our analysis
                      is based on the comparison of space-time profiles of the
                      spin and energy correlation functions, where the agreement
                      is found to hold not only in the bulk but also in the tails
                      of the resulting density distribution. The mean-squared
                      displacement of the density profiles reflects the nature of
                      emerging hydrodynamics and is found to exhibit similar
                      scaling for quantum and classical models.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000891819700004},
      doi          = {10.1103/PhysRevResearch.4.043147},
      url          = {https://juser.fz-juelich.de/record/916119},
}