Separation of variables for nondiagonalizable models: XXX spin chain with twisted boundary conditions
Year: 2026
Type: article
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.
DOI: 10.1103/xlkt-rqhf
Author: Juan Miguel Nieto García
Institution: Universidad Politécnica de Madrid
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7213401073