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PreprintCC BY 4.0arXiv

Extremal States of Multipartite Quantum Spin Systems

  • Oskar Olander
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Abstract

We consider two quantum spin models on k-partite graphs. The system is assumed to be invariant under all permutations within any of the k sets. In the limit of infinitely many particles, the Gibbs state is described as a mixture of independent spins due to a version of the Quantum de Finetti theorem. First, we study a spin-1/2 antiferromagnetic Heisenberg model and identify its three phases. At low temperature all k sets are magnetised but cancel each other, at medium temperature there is a net magnetic field and at high temperature there is no magnetisation. The magnetisation temperature is a solution to a k-degree polynomial. Second, we allow a general spin s and identify all orthogonally invariant models which have frustration. The criterium for a frustration-free model is that the k-sets can be partitioned into two parts, where the only antiferromagnetic interaction is between the two parts.

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Cite

BibTeXRIS
BibTeX
@misc{olander2026extremal,
  title = {{Extremal States of Multipartite Quantum Spin Systems}},
  author = {Oskar Olander},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12873},
  eprint = {2609.12873},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12873},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Extremal States of Multipartite Quantum Spin Systems
AU  - Oskar Olander
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12873
UR  - https://arxiv.org/abs/2609.12873
AB  - We consider two quantum spin models on k-partite graphs. The system is assumed to be invariant under all permutations within any of the k sets. In the limit of infinitely many particles, the Gibbs state is described as a mixture of independent spins due to a version of the Quantum de Finetti theorem. First, we study a spin-1/2 antiferromagnetic Heisenberg model and identify its three phases. At low temperature all k sets are magnetised but cancel each other, at medium temperature there is a net magnetic field and at high temperature there is no magnetisation. The magnetisation temperature is a solution to a k-degree polynomial. Second, we allow a general spin s and identify all orthogonally invariant models which have frustration. The criterium for a frustration-free model is that the k-sets can be partitioned into two parts, where the only antiferromagnetic interaction is between the two parts.
ER  -