Connected correlations in partitioning protocols: a case study and beyond

TL;DR

This paper investigates when local observables in quantum quenches can be accurately described by generalized hydrodynamics, focusing on the role of connected correlations and the conditions for Gaussian behavior in non-interacting systems.

Contribution

It formally establishes the locality conditions under which observables depend only on the root density, clarifying the regime of validity for GHD and Gaussianization in partitioning protocols.

Findings

Connected correlations determine the locality regime for GHD.

Root density suffices to describe certain local observables under specific conditions.

Conditions for Gaussianification are identified based on correlation contributions.

Abstract

The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address formally the question of when an observable is ``local enough'' to be described by GHD using the playground of partitioning protocols and non-interacting time evolution. We show that any state evolving under a quadratic Hamiltonian can be described via a set of decoupled dynamical fields such that one of those fields can be identified with a space-time-dependent generalisation of the root density. By studying the contribution to a connected spin correlation of each of those fields independently, we derive the locality conditions under which an observable can be described using the root density only. That shows both the regime of validity for hydrodynamic approaches that aim at describing the asymptotic value of observables in term of the root density only, such as GHD, and the locality conditions necessary for Gaussianification to occur.