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Inhomogeneous SSH models and the doubling of orthogonal polynomials
by Nicolas Crampé, Quentin Labriet, Lucia Morey, Gilles Parez, Luc Vinet
Submission summary
| Authors (as registered SciPost users): | Lucia Morey |
| Submission information | |
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| Preprint Link: | scipost_202511_00043v1 (pdf) |
| Date submitted: | Nov. 19, 2025, 5:27 p.m. |
| Submitted by: | Lucia Morey |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We analyze Su--Schrieffer--Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of the models. We demonstrate that the standard SSH model is associated with the doubling of Chebyshev polynomials. Extending this technique to the doubling of other finite sequences enables the construction of Hamiltonians for inhomogeneous SSH models which are exactly solvable. We detail the specific cases associated with Krawtchouk and $q$-Racah polynomials. This work highlights the utility of polynomial-doubling techniques in obtaining exact solutions for physical models.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing