Even-Odd Effects of Heisenberg Chains on Long-range Interaction and Entanglement

TL;DR

This paper investigates how the parity of Heisenberg spin chains influences their ability to mediate long-range entanglement and effective interactions between external qubits, revealing parity-dependent phenomena such as maximal entanglement and RKKY interactions.

Contribution

It provides a detailed comparison of even and odd Heisenberg chains, uncovering parity effects on entanglement and interaction mechanisms in quantum communication channels.

Findings

Maximal entanglement occurs in even chains with attached qubits.

RKKY interactions are observed in even chains.

Chains of both parities can mediate distance-independent qubit entanglement.

Abstract

A strongly coupled Heisenberg chain provides an important channel for quantum communication through its many-body ground state. Yet, the nature of the effective interactions and the ability to mediate long-range entanglement differs significantly for chains of opposite parity. Here, we contrast the characters of even and odd-size chains when they are coupled to external qubits. Additional parity effects emerge in both cases, depending on the positions of the attached qubits. Some striking results include (i) the emergence of maximal entanglement and (ii) Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for qubits attached to an even chain, and (iii) the ability of chains of either parity to mediate qubit entanglement that is undiminished by distance.