2011/10/31 by Luc Vinet, Alexei Zhedanov · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP
paper · pdf · doi:10.1103/physreva.85.012323
7 pages
arxiv created 2011/11/16 · arxiv updated 2013/05/29
It is shown how to systematically construct the XX quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST). 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 new model connected to a special case of the symmetric q-Racah polynomials is offered. It is also explained how additional models with PST can be derived from a parent system by removing energy levels from the one-excitation spectrum of the latter. This is achieved through Christoffel transformations and is also completely constructive in regards to the Hamiltonians.