## SciPost Submission Page

# Transport in one-dimensional integrable quantum systems

### by J. Sirker

#### This is not the current version.

### Submission summary

As Contributors: | Jesko Sirker |

Preprint link: | scipost_201910_00039v4 |

Date submitted: | 2020-04-24 |

Submitted by: | Sirker, Jesko |

Submitted to: | SciPost Physics Lecture Notes |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### Abstract

These notes are based on a series of three lectures given at the Les Houches summer school on 'Integrability in Atomic and Condensed Matter Physics' in August 2018. They provide an introduction into the unusual transport properties of integrable models in the linear response regime focussing, in particular, on the spin-1/2 XXZ spin chain.

###### Current status:

### List of changes

1) Outline: I added the sentence 'Furthermore, I also note that a

different approach to transport---generalized hydrodynamics---has been

discussed in a separate series of lectures and will not be covered

here.'

2) End of chapter 1: ' and discuss the general picture emerging from

these calculations as well as their limitations.'

3) End of introduction to chapter 2: 'While we concentrate on these

specific anisotropies in the following, we note that the results can

be generalized to all commensurate anisotropies $\gamma = n\pi/m$ with

$n,m$ coprime. On the other hand, it has been argued that ballistic

transport possibly coexists with superdiffusion at incommensurate

anisotropies while transport is entirely superdiffusive at the

isotropic point, $\Delta=1$ [34].

4) Below Eq. (2.28): 'We note that we have assumed here that the integral in

Eq.~(2.28) is convergent. If this is not the case, then the

additional channel is superdiffusive. As indicated before, this

possibly happens at incommensurate anisotropies but will not be

discussed here further.'

5) Below Eq. (2.28): 'It

provides a strict lower bound---possibly even exhaustive---for

rational $\gamma/\pi$ and thus proof that ballistic transport for

these anisotropies indeed persists at finite temperatures.'

6) Reference to Louis, Gros below Eq. (3.9) added.

7) Experimental reference add below Eq. (3.9).

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2020-5-8 Invited Report

### Strengths

See 1st report

### Weaknesses

See 1st report

### Report

In the revised version, the author has implemented some but not all of the suggestions and

requests from the previous report.

One should stress that the points from the previous report could have been implemented

without much effort, by adding or modifying a few sentences and adding references.

The author dismisses the suggestions using these arguments, paraphrased in my own words:

(i) in the author’s view, the notes should only describe the actual contents

of the author's lecture

(ii) some aspects are mentioned in other lectures of the same school (e.g., GHD) and hence do

not require mentioning

(iii) a fair sampling of e.g. numerics would require "to list many more paper than the three

mentioned by the referee."

(iv) certain topics/methods were not discussed in the lectures.

These arguments are not convincing. Point (i): we are discussing a manuscript that is accessible individually in SciPost and on the arXiv and that can and should be viewed as a stand-alone

article. There is no reason why a lecture and a manuscript should be their exact mirror: one is

accessible to a limited audience, the manuscript is an article available to the public and if

peer-reviewed, subject to the usual standards.

Point (ii): While GHD is covered in other parts of the school, other aspects (e.g., contributions

from numerics) were maybe not covered there. We are not debating adding extensive

discussions, but only references that allow the reader to explore topics on their own that are not covered in the lecture notes.

(iii) If it takes a long list of reference to provide a fair sampling of contributions from numerical methods, then so be it. My comment from the first report did not imply exclusiveness of the

suggested references.

(iv) Precisely because the contents of the lectures cannot cover the whole field, it is essential

that references to those parts that were not covered are provided in the text, in particular, for

students and researchers from outside of the field.

Perhaps the guidelines of the Physical Review on Referencing might be helpful here

(see https://journals.aps.org/prb/authors/editorial-policies-practices):

"Manuscripts must provide proper citations to pertinent earlier work and credit significant contributions by non-authors. Readers benefit from complete referencing, which correctly contextualizes the work in regards to related research. Authors should make every effort to ensure that their citations to previously published work are comprehensive at the time of submission. These citations can include references to books and references to published conference proceedings that contain more than abstracts. Prior to publication, authors should add citations to works published during the course of the review process."

In my understanding, these are generally and widely accepted criteria and are of particular

significance for a review or introductory article such as this manuscript.

The author is therefore advised to implement the remaining suggestions 1), 4), 5), 6), 7) and 8) from the first report – see below for further details.

Furthermore, the author is encouraged the to re-examine the whole manuscript in view of the

guidelines quoted above.

### Requested changes

More detailed comments on the points from the first report that were not implemented:

Ad 1) Numerical methods are actually mentioned and discussed in the manuscript, see the bottom of page 14:

"Numerically, these predictions can be tested by calculating the diffusion constant directly from the current-current correlation function, see Eq. (2.28). In such numerical calculations, the

main problem is to reach sufficiently long times to obtain reliable results for the integral over

the time-dependent current-current correlation function."

Without proper references, this text is useless to readers not familiar with the field or the

literature. The author must provide references to pertinent literature.

In this context, see also page 4: where Ref 34 is cited: Super-diffusion at the isotropic point was first suggested by Znidaric, Phys. Rev. Lett. 106, 220601 (2011).

Ad 4) Discussion of experiments, pages 9/10: Why not cite the most recent review by Hess here? See the first report.

Also, on page 9: "Obtaining a detailed understanding of the heat transport as measured experimentally is, however, a complex and still somewhat open issue. It requires an identification of the dominant relaxation processes and a formalism to incorporate such scattering mechanisms in the calculation of the thermal conductivity."

There is pertinent theoretical literature here as well that should be cited, by Rosch, Chernyshev, Rozhkov, and others. The statement is a dead end for the reader if left without references.

Ad 5) Page 14: The author should add the references mentioned in the first report about Delta >1, Otherwise, the history and contributions of a number of researchers are not properly accounted for. See the sentence

"The quasi-local charges which protect part of the spin current, on the other hand, become non-local for Delta > 1 and the spin transport becomes diffusive"

Ad 6) See the previous report.

Ad 7) The key (and seminal) contribution of the work of Prosen et al. Ref. 7-9 was to discover the quasi-local charges and to relate them to the Drude weight. This contribution should be acknowledged.

For instance, see page 6: Page 6: "These charges are sometimes called quasi-local and play an important role in understanding the spin transport properties of the XXZ chain."

Here, the author should state that these charges were discovered in Prosen PRL 2011 Prosen and Ilievski PRL 2013 (Refs. 7, 8).

Ad 8) See the previous report.

(in reply to Report 1 on 2020-05-08)

In the second report, the referee repeats the points from the first

report. While it is clear that the referee is very passionate about

the requested changes, the report, in my view, does cross a line which

is not helpful. Besides, the report misses that many of the requested

changes have actually been implemented. For the remaining points where

we do disagree, it would have been appropriate, in my view, to reflect

on my arguments instead of dismissing them outright. It is possible to

disagree in a respectful manner.

Since I have already replied to all the points raised in my first

reply and have nothing to add, I will instead summarize some thoughts

in order to move forward. One the one hand, I have some general

remarks about lecture notes which are perhaps worth considering for

the future. On the other hand, I suggest a compromise for this

particular case which, hopefully, allows to bring this long process to

a conclusion.

Let me start with my general remarks: The Les Houches Lecture Notes

are a well established format which is different from a review

journal. Being pedagogical and also reflecting the personal views of a

researcher of a particular research field are, in my view, what makes

them valuable and is why they are often recommended to graduate

students. For the graduate students which attended the school it is,

furthermore, important that the notes do reflect what was actually

taught. For this reason it should also be clear that lecture notes can

never be fully up-to-date. While this school (held in 2018) might be

an extreme case, there will likely always be some delay between the

actual lectures and the date when the corresponding notes are

published. I do not think that there should be any pressure on the

lecturers to include material published after the school was

concluded. I personally feel that it would be a shame to move away

from the established, successful format and to effectively turn the

Les Houches Lecture Notes into yet another review journal.

Coming back to the manuscript at hand: I am facing a bit of a

conundrum here because I am convinced that my lecture notes are

completely in line with the established format. A check of a sampling

notes from previous schools on related topics confirms this. In

particular, I note that most full lecture courses (mine was only a

half a course) - resulting in lecture notes of 30-80 pages - list

40-50 references (of course, there are some exceptions with much fewer

or many more as well). In the latest version of my notes, 41

references are included which therefore is already near the upper end

of the spectrum.

In the main text, I do not want to move away from presenting the

material in a pedagogical way and from selecting the references

accordingly. I also believe that it would be counterproductive to

extend the notes to topics which were not covered in the actual

lectures. As a compromise and in order to move forward, I have now

added an addendum at the end of the notes where additional references

for topics not or only very briefly discussed in my lectures are

given. This includes, in particular, numerical studies of transport in

integrable models and studies of the regime with anisotropy Delta > 1.

I hope that the manuscript in its current form can now be accepted and

published without further delay.