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High temperature series expansions of S = 1/2 Heisenberg spin models: algorithm to include the magnetic field with optimized complexity
by Laurent Pierre, Bernard Bernu, Laura Messio
Submission summary
| Authors (as registered SciPost users): | Laura Messio |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2404.02271v1 (pdf) |
| Code repository: | https://bitbucket.org/lmessio/htse-code/src/main/ |
| Data repository: | https://bitbucket.org/lmessio/htse-coefficients/src/main/ |
| Date submitted: | 2024-04-04 09:55 |
| Submitted by: | Messio, Laura |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
This work presents an algorithm for calculating high temperature series expansions (HTSE) of Heisenberg spin models with spin $S=1/2$ in the thermodynamic limit. This algorithm accounts for the presence of a magnetic field. The paper begins with a comprehensive introduction to HTSE and then focuses on identifying the bottlenecks that limit the computation of higher order coefficients. HTSE calculations involve two key steps: graph enumeration on the lattice and trace calculations for each graph. The introduction of a non-zero magnetic field adds complexity to the expansion because previously irrelevant graphs must now be considered: bridged graphs. We present an efficient method to deduce the contribution of these graphs from the contribution of sub-graphs, that drastically reduces the time of calculation for the last order coefficient (in practice increasing by one the order of the series at almost no cost). Previous articles of the authors have utilized HTSE calculations based on this algorithm, but without providing detailed explanations. The complete algorithm is publicly available, as well as the series on many lattice and for various interactions.
Current status:
Reports on this Submission
Strengths
1) Detailed, step by step presentation of a new algorithm for calculation of the high-temperature series for the general spin-1/2 exchange Hamiltonian with the Zeeman term
Weaknesses
1) introduction is too short and technical
2) no actual results are presented
Report
This is an important theoretical work which extends capability of the high-temperature expansion technique for quantum spin models by including the effect of strong magnetic field. Still a couple of improvements on the manuscript can be made that will increase visibility of the current work within quantum magnetism community. The introduction is extremely short and a bit out of point. Instead of a somewhat ambiguous statement about general validity of the Hubbard model (not studied in this work) authors may give a brief historical overview of the high-temperature expansion methods. For deeper appreciation of their results, authors may also include explicit results for one or two simple spin models. For example, the series obtained for square and kagome lattice antiferromagnets can be used to compute the uniform magnetization M(T,h) for a few values of h ~ J.
Recommendation
Ask for minor revision