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Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
by Giuseppe Del Vecchio Del Vecchio, Benjamin Doyon, Paola Ruggiero
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Giuseppe del Vecchio del Vecchio |
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| Preprint Link: | https://arxiv.org/abs/2301.02326v2 (pdf) |
| Date accepted: | 2024-01-09 |
| Date submitted: | 2023-07-05 23:57 |
| Submitted by: | del Vecchio del Vecchio, Giuseppe |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of \emph{branch-point twist fields}, the starting point for computing R\'enyi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of R\'enyi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations.
Published as SciPost Phys. Core 7, 005 (2024)
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2023-11-21 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2301.02326v2, delivered 2023-11-21, doi: 10.21468/SciPost.Report.8167
Report
In this paper the authors study bipartite entanglement entropies in free fermionic systems, from a field-theoretical perspective. They work in a well-established theoretical framework, by which bipartite entanglement entropies can be related to correlation functions of so-called branch-point twist fields. The original part of the work is to study these correlation functions by means of a hydrodynamic approach, and specifically using the so-called ballistic fluctuation theory (BFT).
In detail, the authors show explicitly that known results on the Renyi entropy at equilibrium and out of equilibrium (after a quench) can be recovered from the BFT. They argue that the formalism leads to a natural interpretation of the mechanisms at the basis of the entanglement growth. One of the main claims of the authors is that large-scale behaviour of entanglement is controlled by large-deviation principles.
Overall, I think the draft is well written and it is always clear what the authors are doing. To the best of my understanding, the calculations are correct and the results are solid.
While the authors claim that the formalism naturally lead to a more transparent interpretation of the entanglement behaviour, the treatment if overall quite technical, and so difficult to appreciate outside of a narrow audience. Therefore, I believe the choice of Scipost Physics Core is appropriate, compared to Scipost Physics.
For the reasons above, I recommend publication of the draft as is.