# Out-of-time ordered correlation functions for the localized $f$ electrons in the Falicov-Kimball model

## TL;DR

This paper calculates exact out-of-time correlation functions for localized $f$ electrons in the Falicov-Kimball model, revealing insights into quantum chaos and scrambling within a mean-field framework.

## Contribution

It provides an exact evaluation of OTOCs for localized electrons in the Falicov-Kimball model using dynamical mean-field theory, highlighting regimes of quantum chaos.

## Key findings

- Different regimes of quantum chaos and scrambling identified.
- OTOCs show similarities with disordered quantum spin models.
- Winding numbers of block Toeplitz matrices characterize chaos regimes.

## Abstract

We provide an exact evaluation of the out-of-time correlation (OTOC) functions for the localized $f$-particle states in the Falicov-Kimball model within dynamical mean-field theory. Different regimes of quantum chaos and quantum scrambling are distinguished by the winding numbers of the block Toeplitz matrices used in the calculation. The similarities of these fermionic OTOCs and their logarithmic derivatives for time evolution with the OTOCs for quantum spin models with disorder are also discussed.