Dynamical generation of alpha-Rényi entropies (0 < alpha <= 1) in one-dimensional local quantum spin systems

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• Daniele Toniolo, UCL
• Thursday 03 April 2025, 14:15-15:15
• MR14.

If you have a question about this talk, please contact Laurens Lootens.

I will discuss the dynamical generation of entanglement, as quantified by alpha-Rényi entropies with 0 < alpha <= 1, including the case alpha=1 of the von Neuman entropy, starting from a generic product state for one-dimensional local quantum spin systems. I will show that this follows from the Lieb-Robinson bound of the dynamics with a quantitative relation. 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 an operator to spread across a region takes a time proportional to the exponential of the size of such region), I will obtain the log t-law of entanglement 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 motions. This is based upon [1] and [2]. A glimpse into the stability of slow dynamics against local perturbations, according to [3], will be also given.

[1] D. Toniolo, S. Bose, https://arxiv.org/abs/2408.00743 [2] D. Toniolo, S. Bose, https://arxiv.org/abs/2408.02016 [3] D. Toniolo, S. Bose, https://arxiv.org/abs/2405.05958

This talk is part of the CQIF Seminar series.

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