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arxiv: 2511.21821 · v2 · pith:3A4NYUX3new · submitted 2025-11-26 · ❄️ cond-mat.mtrl-sci

IRSSG: An Open-Source Software Package for Spin Space Groups

Sheng Zhang , Ziyin Song , Zhong Fang , Hongming Weng , Zhijun Wang This is my paper

Pith reviewed 2026-05-21 17:26 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords spin space groupsmagnetic symmetryDFT wavefunctionsirreducible corepresentationsaltermagnetismmagnetic topologysymmetry softwareband labeling
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The pith

IRSSG software identifies all spin space group operations from DFT wavefunctions and assigns irreducible corepresentation labels to magnetic energy bands.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces an open-source package called IRSSG that analyzes magnetic systems by determining their spin space group symmetries directly from density functional theory wavefunctions. It first finds all symmetry operations and assigns an international symbol, then creates character tables for little groups at chosen momentum points, and finally labels the energy bands with their irreducible corepresentations by calculating representation traces. This tool integrates with popular DFT codes like VASP and Quantum ESPRESSO through Wannier90 interfaces. A sympathetic reader would care because spin space groups capture combined spatial and spin symmetries that govern phenomena such as altermagnetism and protected band degeneracies in magnetic materials.

Core claim

The IRSSG package works within the DFT framework by taking wavefunctions as input. It identifies all SSG operations and determines the SSG international symbol for a given magnetic system. It generates the SSG character tables of little groups at any k point. Finally, it computes the traces of matrix representations of SSG operations and assigns irreducible corepresentation labels to magnetic energy bands.

What carries the argument

IRSSG, the software package that detects spin space group operations by processing DFT wavefunctions and uses trace calculations to label bands with irreducible corepresentations.

If this is right

  • Researchers gain an automated route to study magnons and altermagnetism in systems whose symmetries are described by spin space groups.
  • Character tables become available for little groups at any chosen k-point in magnetic structures.
  • Magnetic energy bands receive systematic irreducible corepresentation assignments based on computed traces.
  • The approach supports direct input from VASP, Quantum ESPRESSO, and Wannier90 outputs for practical calculations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The labeled bands could be used to compute topological invariants that are protected specifically under spin space group symmetries.
  • Scanning material databases with IRSSG might help identify new candidates for high-degeneracy magnetic excitations.
  • Validation on additional test cases with known SSGs would clarify how far the automation extends without manual checks.

Load-bearing premise

The wavefunctions output by standard DFT calculations contain all the information needed to uniquely identify the complete set of spin space group operations without extra inputs on the magnetic configuration.

What would settle it

Running IRSSG on a collinear antiferromagnet with independently known SSG symmetry and verifying whether it recovers the correct international symbol along with accurate band labels.

Figures

Figures reproduced from arXiv: 2511.21821 by Hongming Weng, Sheng Zhang, Zhijun Wang, Zhong Fang, Ziyin Song.

Figure 1
Figure 1. Figure 1: Workflow of IRSSG for spin space groups. Based on the above derivations, the code has been extended to work with the TB Hamiltonians. Thus, it works for any DFT code that has an interface to Wannier90, e.g. VASP, Wien2k [37, 38] and OpenMX [39–41]. To run IRSSG, users must provide two input files: case hr.dat and tbbox.in. The file case hr.dat contains the TB parameters and can be generated by Wannier90 [3… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Magnetic crystal structure of Mn3Sn with coplanar configuration. (b) The modified POSCAR. coordinates should follow the fractional coordinates of the atoms. A 5-tuple variable ‘cell’ as defined in Table III is obtained. For instance, the modified POSCAR file of Mn3Sn with a type-II configuration is shown in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Screenshot of ‘ssg.out’. 1. Obtaining the SSG k-little group The SSG operations are read from ‘ssg.data’ by get ssg.f90. An SSG operation that leaves k invariant up to a reciprocal-lattice vector [Eq. (4)] belongs to the k-little group; this is implemented in kgroup.f90. All related variables are summarized in Table IV in detail. 2. Generating the character table of the k-little group In this part, we use … view at source ↗
Figure 4
Figure 4. Figure 4: (a) Magnetic energy bands of Mn3Sn with a type-II configuration. (b) Screenshot of ‘chart.dat’. 3. Obtaining compatibility relations Due to subgroup relations between the SSG little groups of adjacent k points, the compatibility relations are generated accordingly. They are written to ‘chart.dat’ as well. D. Computing the coirreps of magnetic energy bands For each k point, we obtain the coirreps of all mag… view at source ↗
Figure 5
Figure 5. Figure 5: The band coirreps determined by IRSSG, which are output in ‘irssg.out’. The first three columns give band indices, degeneracies, and energies (without subtracting the Fermi level EF ), respectively. Then the band characters of each unitary operation and the band coirreps are given in the following lines. Panels (a)–(c) correspond to the two DT points (two dash￾dotted lines in [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Magnetic crystal structure of NpBi with a type-III configuration, where Np atoms are magnetic. (b) Magnetic [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Crystal structure of Eu3PbO. (b) Magnetic structure of Eu in Eu3PbO. (c) Magnetic energy bands of Eu3PbO. (fourfold) and GM8 (sixfold), resulting in a high-degeneracy point at the Fermi level. The red line is the highest valence band, while the blue line is the lowest conduction band. All the bands are doubly degenerate due to the presence of two unitary SSG symmetries with the anti-commutation relatio… view at source ↗
read the original abstract

We present an open-source software package IRSSG for investigating magnetic systems with spin space groups (SSGs). The package works within the density functional theory (DFT) framework and requires wavefunctions from DFT codes, such as VASP, Quantum ESPRESSO, as well as any other code that has an interface to Wannier90. We introduce a set of compact SSG international symbols by combining non-crystallographic point groups with the 230 crystallographic space groups. The program first identifies all SSG operations and determines the SSG international symbol for a given magnetic system. It then generates the SSG character tables of little groups at any $k$ point. Finally, it computes the traces of matrix representations of SSG operations and assigns irreducible corepresentation labels to magnetic energy bands. The program is not only timely but also essential for advancing research on the study of magnons, altermagnetism, magnetic topology, and novel high-degeneracy excitations in SSG systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents the open-source IRSSG package for spin space group (SSG) analysis of magnetic systems in the DFT framework. It takes wavefunctions from VASP, Quantum ESPRESSO, or Wannier90 interfaces, identifies all SSG operations and assigns a compact international symbol formed by combining non-crystallographic point groups with the 230 space groups, generates SSG character tables for little groups at arbitrary k-points, computes traces of matrix representations, and assigns irreducible corepresentation labels to magnetic energy bands.

Significance. If the identification and labeling algorithms prove correct, the package would provide a timely automated tool for symmetry analysis in altermagnetism, magnons, and magnetic topology, where manual SSG treatment is currently laborious. The introduction of compact SSG symbols and direct interfacing to standard DFT outputs are practical strengths, but the overall significance cannot yet be assessed without validation data.

major comments (2)
  1. [§3] §3 (SSG identification workflow): The central step of extracting all SSG operations directly from DFT wavefunctions is presented without any benchmark against known SSG cases, test magnetic structures, or discussion of uniqueness for non-collinear or incommensurate order; this is load-bearing because all downstream character tables and corepresentation assignments inherit errors from this step.
  2. [§4] §4 (character table and corepresentation assignment): No explicit validation examples, error-handling details, or comparison to manual SSG calculations or existing codes are provided, so the correctness of the trace computation and irreducible corepresentation labeling cannot be verified from the manuscript.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'compact SSG international symbols' is introduced without a single concrete example or comparison to existing SSG notation.
  2. The manuscript would benefit from a short table listing supported input file formats and output file formats for the character tables and band labels.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript describing the IRSSG package. We address each major comment below and agree that additional validation is needed to strengthen the presentation. Revisions will be made to incorporate benchmarks and examples as detailed in the point-by-point responses.

read point-by-point responses

  1. Referee: [§3] §3 (SSG identification workflow): The central step of extracting all SSG operations directly from DFT wavefunctions is presented without any benchmark against known SSG cases, test magnetic structures, or discussion of uniqueness for non-collinear or incommensurate order; this is load-bearing because all downstream character tables and corepresentation assignments inherit errors from this step.

    Authors: We acknowledge that explicit benchmarks for the SSG identification step are absent from the current manuscript. In the revised version, we will add a dedicated validation subsection that includes benchmarks against known SSG cases (e.g., collinear antiferromagnets and altermagnets), test magnetic structures from the literature, and discussion of operation uniqueness for non-collinear cases. Limitations for incommensurate orders will also be addressed. These additions will allow direct verification of the workflow. revision: yes

  2. Referee: [§4] §4 (character table and corepresentation assignment): No explicit validation examples, error-handling details, or comparison to manual SSG calculations or existing codes are provided, so the correctness of the trace computation and irreducible corepresentation labeling cannot be verified from the manuscript.

    Authors: We agree that the manuscript requires explicit validation for the character table generation and corepresentation labeling. We will include concrete examples comparing computed traces and irreducible corepresentation labels to manual SSG calculations for representative k-points and magnetic systems. Expanded error-handling details and any relevant comparisons to other SSG tools will be added to the text and supplementary material. revision: yes

Circularity Check

0 steps flagged

Software implementation applies established group theory without circular derivation

full rationale

The manuscript describes an open-source software package that implements identification of spin-space-group operations, international symbols, little-group character tables, and irreducible corepresentation labels from DFT wavefunctions. No derivation chain, first-principles prediction, or fitted parameter is presented that reduces by construction to its own inputs. The central workflow is an algorithmic realization of pre-existing group-theoretic concepts (SSG operations combining spin and spatial symmetries) rather than a self-referential or self-citation-dependent theoretical result. The package is self-contained as a computational tool; any uniqueness or completeness issues in operation identification from wavefunctions are matters of algorithmic correctness and input sufficiency, not circularity in a claimed derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The package rests on standard representation theory of spin space groups and the assumption that DFT wavefunctions faithfully encode the magnetic symmetry; no free parameters or new physical entities are introduced beyond the compact notation.

axioms (1)
  • standard math Standard representation theory of spin space groups and little groups applies directly to the magnetic systems under study.
    Invoked when generating character tables and assigning irreducible corepresentations.
invented entities (1)
  • Compact SSG international symbols no independent evidence
    purpose: To label spin space groups by combining non-crystallographic point groups with the 230 crystallographic space groups.
    New notation scheme introduced to make SSG identification more compact.

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Works this paper leans on

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