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Journal of Statistical Physics

Exactly solvable one-dimensional inhomogeneous models

Bernard Derrida, Michel Mendès France, Jacques Peyri�re

Published Nov 1, 1986• 23 citations
Publisher
DOI
10.1007/bf01021080

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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.