18 October 2022 Tue 4 pm

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Krylov state and operator complexities have emerged recently as powerful probes into quantum many-body phenomenon. I will talk about the formalism and various interesting aspects of the same. Then I shall describe the “Universal Operator Growth Hypothesis” which allows for a description of chaotic dynamics via K-complexity.

Using Krylov operator complexity, I will describe some interesting systems which demonstrate saddle-dominated scrambling. Through the study of such systems, I will refine the statement of the operator growth hypothesis and describe some general features of Krylov complexity as a probe of chaotic dynamics.

Using Krylov state complexity, I will describe new insights into the nature of quantum many body scars. I will discuss a refinement of the approximate description of weak ergodicity breaking in such systems. I will also propose a ``tight-binding'' picture which allows an intuitive perspective into the physical nature of scars states.

Finally, I will mention some new results and ongoing work, with regards to the study of complexity and chaos in Floquet systems, field theories and holographic models.

Based on: arXiv:2208.05503, arXiv:2203.03534 and ongoing work.

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