Quantum complexity is now at the forefront of many areas of physics, including high energy physics, condensed matter physics and quantum information. In this talk we will introduce and present results for a relatively new player in the quantum complexity field, indeed a whole new notion of quantum complexity: Krylov complexity. Its definition is organic, it shows interesting properties at short, long and very-long time scales, and it can distinguish integrable from chaotic systems. We will present the so far leading numerical results for Krylov complexity in many-body strongly interacting systems, in particular the maximally chaotic Sachdev-Ye-Kitaev model and the integrable XXZ spin chain, pushing computational limits to the edge of Krylov space.
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Publication:Rabinovici, E., Sánchez-Garrido, A., Shir, R., Sonner, J. Krylov complexity from integrability to chaos. J. High Energ. Phys. 2022, 151 (2022). https://doi.org/10.1007/JHEP07(2022)151 Rabinovici, E., Sánchez-Garrido, A., Shir, R., Sonner J. Krylov localization and suppression of complexity. J. High Energ. Phys. 2022, 211 (2022). https://doi.org/10.1007/JHEP03(2022)211 Rabinovici, E., Sánchez-Garrido, A., Shir, R., Sonner J. Operator complexity: a journey to the edge of Krylov space. J. High Energ. Phys. 2021, 62 (2021). https://doi.org/10.1007/JHEP06(2021)062 Barbón, J., Rabinovici, E., Shir, R., Sinha R. On the evolution of operator complexity beyond scrambling. J. High Energ. Phys. 2019, 264 (2019). https://doi.org/10.1007/JHEP10(2019)264
