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Connected correlations in partitioning protocols: a case study and beyond
by Saverio Bocini
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Submission summary
| Authors (as registered SciPost users): | Saverio Bocini |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202304_00004v1 (pdf) |
| Date accepted: | 2023-05-22 |
| Date submitted: | 2023-04-05 16:32 |
| Submitted by: | Bocini, Saverio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
List of changes
- Some typos and misprints have been fixed
- A paragraph has been added to Section 4 to detail and motivate further the decomposition given in Eqs. 26 and 27.
Section 6.1 has been extended in order to make the asymptotic analysis more explicit. Moreover, I refer more often to the definition of the various functions.
- Section 6.2 was rearranged aiming at more clarity.
- Part of Section 7 was moved to the Appendix and the results are now better stressed out.
- Section 9 has been reorganised in order to clarify what has been conjectured and what has been computed. It is now stressed that Section 9 is independent from Section 8. In particular, the computations that can be carried out but are not shown in Section 8 refer to the fields related to the 4-point correlation function that are not addressed explicitly; on the other hand, Section 9 sketches how one would deal with fields that are related to higher-order correlation functions.
Published as SciPost Phys. 15, 027 (2023)