Inhomogeneous SSH models and the doubling of orthogonal polynomials

TL;DR

This paper employs polynomial doubling techniques to analytically solve inhomogeneous SSH models, linking them to Chebyshev, Krawtchouk, and q-Racah polynomials, and demonstrating their exact solvability.

Contribution

It introduces a polynomial doubling method to construct and solve inhomogeneous SSH models exactly, extending the approach beyond the standard Chebyshev case.

Findings

Standard SSH model linked to Chebyshev polynomial doubling

Extended method constructs exactly solvable inhomogeneous SSH models

Explicit solutions obtained for models related to Krawtchouk and q-Racah polynomials

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.