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

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.

References in corpus (3)

• Many-body localisation implies that eigenvectors are matrix-product states
• Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas
• A uniform area law for the entanglement of eigenstates in the disordered XY chain

Cited by in corpus (9)

• Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
• Low-energy Fock-space localization for attractive hard-core particles in disorder
• Manifestations of dynamical localization in the disordered XXZ spin chain
• Periodic Airy process and equilibrium dynamics of edge fermions in a trap
• On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field
• Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems
• Slow propagation in some disordered quantum spin chains
• Dynamical Evolution of Entanglement in Disordered Oscillator Systems
• Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices