Quantum state transfer on 1-dimensional and 2-dimensional topological Heisenberg spin models

Abstract

The geometrical significance of winding number is used to study the topological characteristics of a single-excitation Heisenberg XY spin model represented by the Su–Schrieffer–Heeger (SSH) model. Due to the presence of topological edge states, the quantum state may be conveyed from the first site to the last site with a high degree of fidelity. Also examined is a Heisenberg XY model on the kagome lattice. In the topological phase of the kagome lattice, the three corner states are not affected by the Dzyaloshinskii–Moriya (DM) interactions. For the kagome lattice with and without the DM interactions, the state of a spin on one corner site can be transferred to the other two corner sites in various ways during the topological phase. The quantum state transfer (QST) for the XY model on the kagome lattice without the DM interactions is symmetrical and can only produce a three-body entangled state. In contrast, the QST for the XY model on the kagome lattice with the DM interactions is in an asymmetrical form, similar to one-way propagation, and it can produce both product states and three-body entangled states.