Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range Interactions Article Swipe
Chi-Chun Zhou
,
Yao Shen
,
Yu-Zhu Chen
,
Wu-Sheng Dai
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2012.12074
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2012.12074
In this paper, we convert the lattice configurations into networks with different modes of links and consider models on networks with arbitrary numbers of interacting particle-pairs. We solve the Heisenberg model by revealing the relation between the Casimir operator of the unitary group and the conjugacy-class operator of the permutation group. We generalize the Heisenberg model by this relation and give a series of exactly solvable models. Moreover, by numerically calculating the eigenvalue of Heisenberg models and random walks on network with different numbers of links, we show that a system on lattice configurations with interactions between more particle-pairs have higher degeneracy of eigenstates. The highest degeneracy of eigenstates of a lattice model is discussed.
Related Topics
Concepts
Eigenvalues and eigenvectors
Degeneracy (biology)
Heisenberg model
Heisenberg group
Lattice (music)
Mathematics
Operator (biology)
Mathematical physics
Quantum mechanics
Pure mathematics
Physics
Statistical physics
Ferromagnetism
Repressor
Biology
Biochemistry
Transcription factor
Gene
Bioinformatics
Acoustics
Chemistry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2012.12074
- https://arxiv.org/pdf/2012.12074
- OA Status
- green
- Cited By
- 1
- References
- 23
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3114994060
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3114994060Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2012.12074Digital Object Identifier
- Title
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Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range InteractionsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2020Year of publication
- Publication date
-
2020-12-22Full publication date if available
- Authors
-
Chi-Chun Zhou, Yao Shen, Yu-Zhu Chen, Wu-Sheng DaiList of authors in order
- Landing page
-
https://arxiv.org/abs/2012.12074Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2012.12074Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2012.12074Direct OA link when available
- Concepts
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Eigenvalues and eigenvectors, Degeneracy (biology), Heisenberg model, Heisenberg group, Lattice (music), Mathematics, Operator (biology), Mathematical physics, Quantum mechanics, Pure mathematics, Physics, Statistical physics, Ferromagnetism, Repressor, Biology, Biochemistry, Transcription factor, Gene, Bioinformatics, Acoustics, ChemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
- Citations by year (recent)
-
2021: 1Per-year citation counts (last 5 years)
- References (count)
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23Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.modes | 12 |
| abstract_inverted_index.solve | 27 |
| abstract_inverted_index.walks | 78 |
| abstract_inverted_index.group. | 50 |
| abstract_inverted_index.higher | 100 |
| abstract_inverted_index.links, | 85 |
| abstract_inverted_index.models | 17, 75 |
| abstract_inverted_index.paper, | 2 |
| abstract_inverted_index.random | 77 |
| abstract_inverted_index.series | 62 |
| abstract_inverted_index.system | 90 |
| abstract_inverted_index.Casimir | 37 |
| abstract_inverted_index.between | 35, 96 |
| abstract_inverted_index.convert | 4 |
| abstract_inverted_index.exactly | 64 |
| abstract_inverted_index.highest | 105 |
| abstract_inverted_index.lattice | 6, 92, 111 |
| abstract_inverted_index.models. | 66 |
| abstract_inverted_index.network | 80 |
| abstract_inverted_index.numbers | 22, 83 |
| abstract_inverted_index.unitary | 41 |
| abstract_inverted_index.consider | 16 |
| abstract_inverted_index.networks | 9, 19 |
| abstract_inverted_index.operator | 38, 46 |
| abstract_inverted_index.relation | 34, 58 |
| abstract_inverted_index.solvable | 65 |
| abstract_inverted_index.Moreover, | 67 |
| abstract_inverted_index.arbitrary | 21 |
| abstract_inverted_index.different | 11, 82 |
| abstract_inverted_index.revealing | 32 |
| abstract_inverted_index.Heisenberg | 29, 54, 74 |
| abstract_inverted_index.degeneracy | 101, 106 |
| abstract_inverted_index.discussed. | 114 |
| abstract_inverted_index.eigenvalue | 72 |
| abstract_inverted_index.generalize | 52 |
| abstract_inverted_index.calculating | 70 |
| abstract_inverted_index.eigenstates | 108 |
| abstract_inverted_index.interacting | 24 |
| abstract_inverted_index.numerically | 69 |
| abstract_inverted_index.permutation | 49 |
| abstract_inverted_index.eigenstates. | 103 |
| abstract_inverted_index.interactions | 95 |
| abstract_inverted_index.configurations | 7, 93 |
| abstract_inverted_index.particle-pairs | 98 |
| abstract_inverted_index.conjugacy-class | 45 |
| abstract_inverted_index.particle-pairs. | 25 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |