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arXiv:2512.12419

Perfect state transfer in inhomogeneous XX model of q-Racah type

Nicolas Crampé, Lafrance, Simon, Charles Robillard, Luc Vinet

Published Dec 13, 2025• 0 citations
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Abstract

New exactly solvable one-dimensional XX spin chain models that exhibit perfect state transfer are defined. These models have inhomogeneous couplings and magnetic fields determined from the three-term recurrence relations satisfied by the q-Racah and para q-Racah polynomials. Due to this connection with orthogonal polynomials, the one-excitation sector can be solved analytically. This allows us to provide explicit sets of conditions on the polynomial parameters that guarantee the occurrence of perfect state transfer across these spin chains.

DOI
10.48550/arxiv.2512.12419

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A method to systematically construct the XXXXXX quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST) is shown. Sets of orthogonal polynomials (OPs) are in correspondence with such systems. The key observation is that for any admissible one-excitation energy spectrum, the weight function of the associated OPs is uniquely prescribed. This entails the complete characterization of these PST models with the mirror-symmetry property arising as a corollary. A simple and efficient algorithm to obtain the corresponding Hamiltonians is presented. A model connected to a special case of the symmetric qqq-Racah polynomials is offered. An explanation of how additional models with PST can be derived from a parent system by removing energy levels from the one-excitation spectrum of the latter is given. This is achieved through Christoffel transformations and is also completely constructive in regards to the Hamiltonians.
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