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SUMMARY:Dynamical generation of alpha-Rényi entropies (0 &lt\; alpha &lt\
 ;= 1) in one-dimensional local quantum spin systems - Daniele Toniolo\, UC
 L
DTSTART:20250403T131500Z
DTEND:20250403T141500Z
UID:TALK229873@talks.cam.ac.uk
CONTACT:Laurens Lootens
DESCRIPTION:I will discuss the dynamical generation of entanglement\, as q
 uantified by alpha-Rényi entropies with 0 < alpha <= 1\, including the ca
 se alpha=1 of the von Neuman entropy\, starting from a generic product sta
 te for one-dimensional local quantum spin systems. I will show that this f
 ollows from the Lieb-Robinson bound of the dynamics with a quantitative re
 lation. For a generic local spin system in one dimension the entanglement 
 grows at most linearly in time. On the other hand when a slow dynamics is 
 considered\, like the one given by a logarithmic lightcone (meaning that a
 n operator to spread across a region takes a time proportional to the expo
 nential of the size of such region)\,  I will obtain the log t-law of enta
 nglement that has been shown before for many-body localized systems mostly
  by numerics or by assuming the existence of a set of local integrals of m
 otions. This is based upon [1] and [2]. A glimpse into the stability of sl
 ow dynamics against local perturbations\, according to [3]\, will be also 
 given.\n\n[1] D. Toniolo\, S. Bose\, https://arxiv.org/abs/2408.00743\n[2]
  D. Toniolo\, S. Bose\, https://arxiv.org/abs/2408.02016\n[3] D. Toniolo\,
  S. Bose\, https://arxiv.org/abs/2405.05958
LOCATION:MR14
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