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  • Open Access

Separation of variables for nondiagonalizable models: XXX spin chain with twisted boundary conditions

Juan Miguel Nieto García*

  • Departamento de Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones, ETSIS de Telecomunicación, Universidad Politécnica de Madrid, Calle Nikola Tesla s/n 28031, Madrid, Spain

  • *Contact author: juanmiguel.nietogarcia@upm.es
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Phys. Rev. D 114, 086024 – Published 30 October, 2026

DOI: https://doi.org/10.1103/xlkt-rqhf

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 generalized eigenvectors of this system can be characterized in terms of a modified TQ equation that we have named the “Jordanian TQ equation.” We also show that the wave function in the separated basis is only separable for true eigenvectors, while the wave function for generalized eigenvectors of higher rank is given instead by a sum over weak compositions.

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Phys. Rev. D 114, 086024– Published 30 October, 2026
  • Received 25 September 2026
  • Accepted 9 October 2026
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