Decay of Determinantal and Pfaffian Correlation Functionals in One-dimensional Lattices

TL;DR

This paper proves bounds on the decay of multipoint correlation functionals in one-dimensional fermionic systems, leading to results on exponential dynamical localization in disordered XY-spin chains.

Contribution

It introduces new bounds on determinants and pfaffians that extend beyond Hadamard estimates, enabling analysis of correlation decay and localization.

Findings

Established bounds on correlation functional decay.

Proved exponential dynamical localization in disordered XY-spin chains.

Extended mathematical tools for analyzing fermionic correlations.

Abstract

We establish bounds on the decay of time-dependent multipoint correlation functionals of one-dimensional quasi-free fermions in terms of the decay properties of their two-point function. At a technical level, this is done with the help of bounds on certain bordered determinants and pfaffians. These bounds, which we prove, go beyond the well-known Hadamard estimates. Our main application of these results is a proof of strong (exponential) dynamical localization of spin-correlation functions in disordered $XY$-spin chains.