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A journey to the edge of Krylov space

ORAL

Abstract

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<br>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<br>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<br>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

Presenters

  • Ruth Shir

    University of Luxembourg

Authors

  • Ruth Shir

    University of Luxembourg

  • Eliezer Z Rabinovici

    Hebrew University of Jerusalem

  • Julian Sonner

    University of Geneva

  • Adrian Sánchez-Garrido

    University of Geneva

  • José Barbón

    Instituto de Fisica Teorica IFT-UAM/CSIC

  • Ritam Sinha

    Hebrew University of Jerusalem