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The SpinParser software for pseudofermion functional renormalization group calculations on quantum magnets
by Finn Lasse Buessen
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Submission summary
Authors (as registered SciPost users):  Finn Lasse Buessen 
Submission information  

Preprint Link:  https://arxiv.org/abs/2109.13317v1 (pdf) 
Code repository:  https://github.com/fbuessen/SpinParser 
Date submitted:  20211006 20:25 
Submitted by:  Buessen, Finn Lasse 
Submitted to:  SciPost Physics Codebases 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
We present the SpinParser opensource software [ https://github.com/fbuessen/SpinParser ]. The software is designed to perform pseudofermion functional renormalization group (pfFRG) calculations for frustrated quantum magnets in two and three spatial dimensions. It aims to make such calculations readily accessible without the need to write specialized program code; instead, custom lattice graphs and microscopic spin models can be defined as plaintext input files. Underlying symmetries of the model are automatically analyzed and exploited by the numerical core written in C++ in order to optimize the performance across largescale shared memory and/or distributed memory computing platforms.
Current status:
Reports on this Submission
Report 2 by Johannes Hauschild on 2022110 (Invited Report)
 Cite as: Johannes Hauschild, Report on arXiv:2109.13317v1, delivered 20220110, doi: 10.21468/SciPost.Report.4166
Strengths
1The library provides a flexible implementation of the pfFRG algorithm capable of dealing with quite generic lattices and interactions.
At the same time, the library is made efficient by exploiting symmetries and providing MPI parallelization.
The blackbox like interface makes it easy to run the code even without detailed knowledge of all the details of pfFRG.
2Both the manuscript and the user guide of the library are well written with examples explaining the typical use cases.
Weaknesses
1In the introduction, it is explained that pfFRG becomes exact in the limit of large spin S. However, as far as I understand, only Spin 1/2 is supported by the current implementation. Please clarify this in the manuscript, and possibly also in the user guide/ReadMe.
(A generalization to higher spin would be nice but is certainly not a requirement for a publication.)
Report
The library and manuscript easily meet all the acceptance criteria.
As the first open implementation of pfFRG, it will certainly be useful to the community.
I therefore recommend a publication after a very minor revision.
Requested changes
See Weakness section above.
Typos:
 duplicated "typically" at end of page 20
 Reference to Sec. 6 instead of 5 in the outline at end of Sec. 1.
Anonymous Report 1 on 2021121 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2109.13317v1, delivered 20211201, doi: 10.21468/SciPost.Report.3952
Strengths
1 The Spin Parser open source software is extremely versatile as it is able to address any given twospin interaction Hamiltonian defined on generic two and threedimensional lattices which can be constructed in custom fashion. This is in addition to the already provided constructions for standard models and lattices.
2 The field of frustrated quantum magnetism poised with the arrival of materials and models which promise to host quantum spin liquid behavior especially in threedimensions. The availability of this software opens the avenues to the entire community of quantum magnetism researchers (theoreticians and experimentalists alike) to access the powerful pfFRG framework which has established itself in being able to provide valuable insights into spin models in 3D, both isotropic and the highly involved spin anisotropic Hamiltonians, which in 3D remain outofreach of most numerical approaches. In being able to compute static susceptibilities the method reaches out to experimentalists and will prove to be an extremely valuable tool for neutron scatterers.
3 The code is heavily optimized in not only exploiting both real space and spin space symmetries in conjunction, but also in providing an excellent performance when deployed on shared and/or distributed memory compute nodes.
4 The manuscript documents all aspects of the open source software in a very systematic and explicit fashion. This makes it user friendly. It also provides a nice and pragmatic introduction to the pfFRG framework, which conveys and appropriately highlights all the essential points and quickly introduces one to a working knowledge of the same.
Weaknesses
1 The Spin Parser software is designed in such a way that its working is restricted to lattices in which all sites a equivalent, i.e., an arbitrary site can be mapped to a given "origin" by employing translations and point group operations. This unfortunately excludes the family of nonArchimedean lattices, which contain ninequivalent sites. Given the fact that some of them, e.g., the squarekagome lattice, and bitrillium lattices have recently come into limelight experimentally in showing evidence for quantum spin liquid behavior [see https://www.nature.com/articles/s4146702017235z, and https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.157204], it may be worthwhile to consider extending the Spin Parser software such that its able to address nonArchimedean geometries.
I understand that this will increase the computational effort as the spinspin correlations in real space would now have to computed from the "n" different/inequivalent origin sites, and also the selfenergy will acquire an additional index, however, from a symmetry reduction point of view this does not add much complication. iF I understand the current implementation, this task seems feasible without much effort. The increase in computational effort is also moderate as most cases of interest involve, e.g., 2 distinct origins, and in general this aspect can be parallelized.
2 In the case of three dimensional lattices with a basis, like the pyrochlore lattice, it is very important that the manuscript/documentation mention that the Hamiltonian in pfFRG is defined in the local frame of reference/basis, and not the global one. This is so because when producing the susceptibility plots to compare with neutron scattering data, one has to carry out a transformation of coordinates to produce the data in the global frame which can then be compared to neutron scattering profiles. The current data output given by the code is in the local frame of reference.
3 Since this manuscript will serve to be a very valuable tool to experimental groups also, it may prove helpful if the code output is slightly redesigned to produce the susceptibility data in both the spinflip and non spinflip channels. From the way the current output files are written, it proves a bit cumbersome to do this postprocessing of data.
4 The current implementation is restricted to spin S=1/2 moments for arbitrary two body Hamiltonians, and works for spin S>1/2 only for Heisenberg models. Maybe I missed some aspect, but I was curious what issues in the implementation would arise if one has S>1/2 moments interacting with a generic anisotropic interaction.
Report
I would be grateful if the author could please take into consideration the remarks I put forth in the Weaknesses section. I would not classify them strictly as weaknesses or shortcomings but in my assessment, these are suggestions which are likely to aid towards making the Spin Parser of wider utility, usefulness, and reach to the broad community and thus enhance its impact.
I have gone through the Acceptance Criteria of "SciPost Physics Codebases" and in my opinion, all these criteria are very well met.
Overall, I would strongly recommend the publication of this manuscript and software in SciPost Physics Codebases. However, it would be nice If the author could at least incorporate some of the points mentioned in the weaknesses section, and resubmit a revised manuscript and code. If these seem not feasible, it would be great to have the author's response to these recommendations explaining what issues arise.
Requested changes
Points 14 in the Weaknesses section.
Author: Finn Lasse Buessen on 20220222 [id 2241]
(in reply to Report 1 on 20211201)
Thank you for your thoughtful feedback and for your suggestions for further improvement of the manuscript. Detailed answers to each of your comments are provided below.
1 The restriction to Archimedean lattices indeed excludes application to some spin models which may be of interest. As you correctly point out, an extension of the pfFRG algorithm to cover also nonArchimedean lattices is straightforward on the conceptual level. However, such an extension would also imply significant changes to the numerical backend of the software since the structure of the flow equations themselves would change significantly; the changes would require extensive code testing and validation of the added use cases, while ensuring that the performance for Archimedean lattices is not negatively impacted. Since such an extension would not affect the frontend of the SpinParser software (i.e., the format in which lattice spin models and computational tasks are defined), I believe that it is appropriate to publish the software in its current state and pursue the extension to nonArchimedean lattices in a future revision of the code; already in its current state, the software is applicable to a plethora of spin models of current interest and can be of great use to the community.
2 Thank you for catching this potential source of confusion. I have added a paragraph in Section 5.3 (“Definition of spin interactions”) to clarify the definition of spin operators and their frame of reference. I further added brief remarks below Eq. (4) (i.e., the definition of the twospin correlation function) and in the fourth paragraph of Section 5.4 (“Output data”) to mention this subtlety. Similarly, I have added a paragraph in the “Prepare a task file” section of the quick start guide in the code documentation.
3 Thank you for bringing up the question about the storage format of output data and potential usability issues. The output files generated by SpinParser contain the full set of realspace resolved twospin correlations, which indeed require some postprocessing to relate to typically probed physical quantities. To simplify postprocessing, a set of Python tools that provides convenient access to the correlation functions both in real space and in momentum space (via Fourier transformation) is included with the SpinParser software. In order to make the Python tools more accessible, I have added a separate user documentation for the Python tools [https://fbuessen.github.io/SpinParser/docpython], which is also referenced in the README. Furthermore, to aid experimentalists in computing more complicated correlation functions like the expressions for spinflip and non spinflip scattering, I have added an extra paragraph and example code in the “Evaluate SpinParser output and measurements” section of the README, which illustrates a convenient way to compute such expressions in a few lines of Python code.
4 The extension of the pfFRG algorithm to arbitrary spin length S has originally been proposed in [PRB 96, 045144 (2017)] for Heisenberg models. The spinS generalization contains some pitfalls that make it less suited for spin models with lowered symmetry. Like the original pfFRG scheme, the extension is based on a representation of spin operators in terms of pseudofermions: The S>1/2 operators are first decomposed into multiple replicas of S=1/2 operators, which are then represented by multiple flavors of pseudofermions. However, for this representation to be faithful, all S=1/2 replicas (all pseudofermion flavors) must locally align in a ferromagnetic fashion. As demonstrated in [PRB 96, 045144 (2017)], this tends to happen naturally for Heisenberg models; the alignment constraint can be verified or energetically enforced by adding an onsite coupling term A*S^2, which would energetically punish the unphysical lowerspin sectors of the (replica) pseudofermion representation for some A>0. The constant A needs to be chosen large enough to enforce the constraint, yet it cannot be chosen too large, since that would interfere with the ability to (accurately) numerically resolve the physical exchange couplings of interest. The question of whether meaningful physical results can be produced in a similar way for spin models with nonHeisenberg interactions, which would often favor noncollinear alignment of spins, has not yet been studied. Since the focus of the SpinParser software is to make established and well understood pfFRG techniques readily available, a formal spinS generalization for nonHeisenberg models is not implemented.
Author: Finn Lasse Buessen on 20220222 [id 2240]
(in reply to Report 2 by Johannes Hauschild on 20220110)Thank you for your careful reading of the manuscript and for the very positive assessment of the work, as well as for spotting the typos.
Regarding the question of whether calculations for generalized spinS models are possible: A generalization of pfFRG calculations to spinS Heisenberg models has been proposed in [PRB 96, 045144 (2017)] (see also the response to “Anonymous Report 1 on 2021121”). This generalization is implemented in the SpinParser code, but it had not been documented appropriately before. In the revised manuscript, I have added a paragraph in Section 5.1 (“Structure of a task file”) which provides instructions on how to perform such generalized spinS calculations for Heisenberg models. Furthermore, I have updated the example that is showcased in the “Quick start” section of the README to include a discussion of the spinS generalization.