Quantum State Transfer in a Two-dimensional Regular Spin Lattice of Triangular Shape

TL;DR

This paper analyzes quantum state transfer in a 2D triangular spin lattice with non-uniform couplings, providing exact solutions and demonstrating conditions for perfect transfer from the apex to the boundary.

Contribution

It introduces an exact solution for one-excitation dynamics in a 2D triangular lattice using 2-variable Krawtchouk polynomials, revealing conditions for perfect quantum state transfer.

Findings

Exact solution for one-excitation dynamics using orthogonal polynomials

Identification of parameter conditions for perfect state transfer

Demonstration of transfer from apex to boundary in the lattice

Abstract

Quantum state transfer in a triangular domain of a two-dimensional, equally-spaced, spin lat- tice with non-homogeneous nearest-neighbor couplings is analyzed. An exact solution of the one- excitation dynamics is provided in terms of 2-variable Krawtchouk orthogonal polynomials that have been recently defined. The probability amplitude for an excitation to transit from one site to another is given. For some values of the parameters, perfect transfer is shown to take place from the apex of the lattice to the boundary hypotenuse.