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PreprintCC BY 4.0arXiv

Separation of variables for non-diagonalisable models: XXX with twisted boundary conditions

  • Juan Miguel Nieto García
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Abstract

We study the Heisenberg XXX spin chain with twisted periodic boundary conditions with a defective twist matrix. Using quantum separation of variables, we show that the generalised eigenvectors of this system can be characterised in terms of a modified TQ equation that we have named "Jordanian TQ equation". We also show that the wavefunction in the separated basis is only separable for true eigenvectors, while the wavefunction for generalised eigenvectors of higher rank is given instead by a sum over weak compositions.

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Cite

BibTeXRIS
BibTeX
@misc{garcia2026separation,
  title = {{Separation of variables for non-diagonalisable models: XXX with twisted boundary conditions}},
  author = {Juan Miguel Nieto García},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16146},
  eprint = {2609.16146},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16146},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Separation of variables for non-diagonalisable models: XXX with twisted boundary conditions
AU  - Juan Miguel Nieto García
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.16146
UR  - https://arxiv.org/abs/2609.16146
AB  - We study the Heisenberg XXX spin chain with twisted periodic boundary conditions with a defective twist matrix. Using quantum separation of variables, we show that the generalised eigenvectors of this system can be characterised in terms of a modified TQ equation that we have named "Jordanian TQ equation". We also show that the wavefunction in the separated basis is only separable for true eigenvectors, while the wavefunction for generalised eigenvectors of higher rank is given instead by a sum over weak compositions.
ER  -