The Chirality operators for Heisenberg Spin Systems

TL;DR

This paper introduces a chirality operator for Heisenberg spin chains, revealing a non-zero chirality in odd-site systems that indicates non-coplanar spin arrangements and handedness, with implications for quantum spin system analysis.

Contribution

The paper explicitly constructs the chirality operator as a spin-1/2 operator using permutation operators, providing a new tool for analyzing spin system properties.

Findings

Ground states of odd-site chains exhibit chiral degeneracy.

Non-zero chirality indicates non-coplanar spin configurations.

Chirality operator is explicitly expressed in terms of spin and permutation operators.

Abstract

The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a two-fold Kramers degeneracy. A non-zero chirality implies that the spins are not coplanar, and is a measure of handedness. The chirality operator, which can be treated as a spin-1/2 operator, is explicitly constructed in terms of the spin operators, and is given as commutator of Permutation operators.