Exact out-of-time-ordered correlation functions for an interacting lattice fermion model

TL;DR

This paper derives exact out-of-time-ordered correlation functions for the Falicov-Kimball lattice fermion model using advanced theoretical methods, revealing interaction effects near phase transitions and proposing experimental measurement techniques.

Contribution

It provides the first exact solutions for OTOCs in an interacting lattice fermion model, extending nonequilibrium dynamical mean-field theory to this context.

Findings

OTOC is maximized near the metal-insulator transition.

High-temperature OTOC remains finite and interaction-dependent.

Proposes experimental measurement of fermionic OTOCs in ultracold atoms.

Abstract

Exact solutions for local equilibrium and nonequilibrium out-of-time-ordered correlation (OTOC) functions are obtained for a lattice fermion model with on-site interactions, namely the Falicov-Kimball (FK) model, in the large dimensional and thermodynamic limit. Our approach is based on the nonequilibrium dynamical mean-field theory generalized to an extended Kadanoff-Baym contour. We find that the density-density OTOC is most enhanced at intermediate coupling around the metal-insulator phase transition. In the high-temperature limit, the OTOC remains nontrivially finite and interaction-dependent, even though dynamical charge correlations probed by an ordinary response function are completely suppressed. We propose an experiment to measure OTOCs of fermionic lattice systems including the FK and Hubbard models in ultracold atomic systems.