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Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
by Oleksandr Gamayun, Arthur Hutsalyuk, Balázs Pozsgay, Mikhail B. Zvonarev
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Submission summary
Authors (as registered SciPost users):  Oleksandr Gamayun · Balázs Pozsgay 
Submission information  

Preprint Link:  https://arxiv.org/abs/2301.13840v2 (pdf) 
Date submitted:  20230418 13:55 
Submitted by:  Pozsgay, Balázs 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We investigate finite temperature spin transport in one spatial dimension by considering the spinspin correlation function of the Hubbard model in the limiting case of infinitely strong repulsion. We find that in the absence of bias the transport is diffusive, and derive the spin diffusion constant. Our approach is based on asymptotic analysis of a Fredholm determinant representation. The obtained results are in agreement with Generalized Hydrodynamics approach.
Current status:
Reports on this Submission
Anonymous Report 2 on 2023529 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2301.13840v2, delivered 20230529, doi: 10.21468/SciPost.Report.7265
Strengths
 very impressive exact calculations of a quasiinteracting model
 first explicit check of a spin diffusion constants in integrable systems by means of wave function expression
Weaknesses
 not many just minor points
Report
This is the first check of the expression for the Onsager matrix obtained in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.160603 directly via the miscroscopic wave function in an interacting integrable model. The calculations are clean and well presented, definitely a work to be published in SciPost. Here minor comments:
 first, it would be better to stress that eq 103 has been derived first and only in the following paper, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.160603 , with this one as its long version https://scipost.org/10.21468/SciPostPhys.6.4.049. There is a common misunderstanding stated here in the introduction: GHD is not a tool to compute diffusion constants (but rather a theory that needs the input of the exact form of the diffusion constants). The latter has been computed first using a form factor expansion (in the two references above), then later also by hydrodynamic projection and kinetic theory, never by "GHD".
 Can the author compute integrated currentcurrent correlator also, in order to obtain the Onsager matrix?
 Can the authors give an analytical expression for the "diffusion constant" at finite time, i.e. figure 1 inset? It would be a nice addition.
 Why is rho = 2/3 at infinite temperature?
 I cannot see where the scattering T in eq 97 is derived
 Could the author's comment on the 1/U correction ? Spin diffusion constant is indeed expected to be infinite at finite U and zero magnetisation.
 Section 5 i would rather call it
"Thermodynamic of the model and GHD diffusion constant". It would also be nice to make clear how to derive the TBA of the model from the large U limit of the TBA of the Hubbard model.
Requested changes
see report
Strengths
1interesting model
2actual interest
3exact calculation
4well written
Weaknesses
1missing comparison with other calculations
2missing physical information
3what means "absence of bias" in the abstract ?
Report
The authors present an evaluation of the spinspin correlation function at finite temperature in the infiniteU 1D Hubbard model. The exact result is in the form of Fredholm determinants
that must in the end be evaluated numerically.
They give long time asymptotic expressions from which they extract the Drude weight and diffusion constant.
The compare their results with the those obtained from the GHD approach.
I think it would be useful to also compare them with results from Mazur bound in the high temperature limit which are transparent and very easy to obtain.
Although it is a rather mathematical study, it would be very interesting to present and discuss physical results on the Drude weight and diffusion constant e.g. as a function of temperature, magnetic field (magnetization).
After these additions/discussion I recommend publication in this journal.