Connected correlations in partitioning protocols: a case study and beyond

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.

38+14 pages, 6+3 figures; typos corrected

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Cited by in corpus (5)

• Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
• Quantum fluctuating theory for one-dimensional shock waves
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Asymptotic behaviour of determinants through the expansion of the Moyal star product
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State