Detecting quantum chaos through eigenstate deformations

In this talk I will show how quantum geometric tensor or fidelity susceptibility can be used as a sensitive probe of quantum chaos. In particular, I will show that using this probe one can detect very small integrability breaking perturbations. I will also discuss that ergodic and integrable regimes are generically separated by an intermediate phase characterized by the maximum possible sensitivity of eigenstates to small perturbations and by exponentially slow in the system size dynamics. I will apply this probe to various clean and disordered models and in particular show a strong evidence that many-body localization is unstable in the thermodynamic limit.

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