Quantum spin chains with fractional revival

TL;DR

This paper systematically analyzes fractional revival in XX quantum spin chains, presenting analytic models with two parameters where revival time is independent of chain length, combining isospectral deformations and para-Krawtchouk polynomial properties.

Contribution

It introduces new analytic models for fractional revival in spin chains, linking isospectral deformations and orthogonal polynomial recurrence coefficients.

Findings

Models exhibit fractional revival at two sites with length-independent revival time.

Combines two methods: isospectral deformations and para-Krawtchouk polynomial properties.

Models can also exhibit perfect state transfer alongside fractional revival.

Abstract

A systematic study of fractional revival at two sites in $XX$ quantum spin chains is presented and analytic models with this phenomenon are exhibited. The generic models have two essential parameters and a revival time that does not depend on the length of the chain. They are obtained by combining two basic ways of realizing fractional revival in a spin chain each bringing one parameter. The first proceeds through isospectral deformations of spin chains with perfect state transfer. The second arises from the recurrence coefficients of the para-Krawtchouk polynomials with a bi-lattice orthogonality grid. It corresponds to an analytic model previously identified that can possess perfect state transfer in addition to fractional revival.