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Locally quasi-stationary states in noninteracting spin chains

by Maurizio Fagotti

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Submission summary

Authors (as registered SciPost users): Maurizio Fagotti
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-03-05
Date submitted: 2020-02-26 01:00
Submitted by: Fagotti, Maurizio
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").

Author comments upon resubmission

The manuscript has been improved following the referees' comments; in addition, some parts have been refined. The main changes are in sections 1.1, 3.4, and 4.

In section 1.1 I've clarified the problems that were undermining generalised hydrodynamics, explaining, in particular, the issues found in Ref. [84]. I've also commented on the gauge choice of Refs [79][80].

In the original version of the manuscript, the solution to the dynamics in the presence of Hamiltonian inhomogeneities was arguably unsatisfactory; I resolved this issue by rewriting part of section 3.4 (section 3.3 of the original version).

Section 4 has been expanded to include a numerical check of the theory. Specifically, I used a trick to adapt the results of the manuscript to finite chains with periodic boundary conditions on the Jordan-Wigner fermions; this has allowed me to numerically test the predictions in finite chains, finding perfect agreement. I've also shown the error made by truncating generalised hydrodynamics at a given order.

Overall, I've taken into consideration the referees' recommendations and I've also made changes to resolve the weaknesses pointed out by referee 2. I think that the new version of the manuscript is a substantial improvement on the original version, and I am confident that the referees will appreciate the changes.

List of changes

1. Some typos have been fixed.
2. Section 1.1 has been improved.
3. To avoid misunderstanding, in section 2 some sentences have been rephrased.
4. The terminology "global/local root density" and "global/local auxiliary field" has been revised. The quantities are now called "spuriously local" instead of "global" and "genuinely local" instead of "local".
5. For the sake of simplicity, some irrelevant comments in Section 2 have been removed.
6. A short subsection called "Expectation values" has been added after 3.2; it contains some pre-existent material of the original version (section 3.2) and something new.
7. Section 3.4 (i.e. section 3.3 of the original version) has been substantially improved.
8. A subsection has been created in section 4. It reports a numerical check of the analytical predictions.
9. Three references have been added: [88], [89], and [91].

Published as SciPost Phys. 8, 048 (2020)

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