Exactly solvable inhomogeneous XY spin chain
Mathematical Physics
2025-07-10 v1 math.MP
Abstract
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jordan-Wigner transformation. Finding the spectrum of such models amounts to diagonalizing a matrix whose size is equal to the number of sites in the chain. This is achieved by recognizing and exploiting contiguity relations satisfied by specific orthogonal polynomials.
Keywords
Cite
@article{arxiv.2507.06331,
title = {Exactly solvable inhomogeneous XY spin chain},
author = {Pierre-Antoine Bernard and Nicolas Crampé and Quentin Labriet and Lucia Morey and Luc Vinet},
journal= {arXiv preprint arXiv:2507.06331},
year = {2025}
}
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8 pages