Yangian symmetry in molecule {V6} and four-spin Heisenberg model

TL;DR

This paper explores Yangian symmetry in molecular spin systems, specifically in the V6 molecule and a four-spin Heisenberg model, revealing how such symmetry influences ground states and magnetization properties.

Contribution

It introduces a Yangian symmetry operator for Heisenberg spin triangles and extends the analysis to a four-spin model, predicting ground state spins and magnetization in theoretical molecules.

Findings

Ground state can have total spin S=1 with suitable exchange constants.

Yangian symmetry relates to the Dzyaloshiky-Moriya interaction in spin systems.

Predicted local magnetic moments in the theoretical V15-like molecule.

Abstract

The symmetry operator $Q=Y^2$ is introduced to re-describe the Heisenberg spin triangles in the \{V6\} molecule, where $\mathbf{Y}$ stands for the Yangian operator which can be viewed as special form of Dzyaloshiky-Moriya (DM) interaction for spin 1/2 systems. Suppose a parallelogram Heisenberg model that is comprised of four 1/2-spins commutes with $Q$, which means that it possesses Yangian symmetry, we show that the ground state of the Hamiltonian $H_4$ for the model allows to take the total spin S=1 by choosing some suitable exchange constants in $H_4$. In analogy to the molecular \{V6\} where the two triangles interact through Yangian operator we then give the magnetization for the theoretical molecule "\{V8\}" model which is comprised of two parallelograms. Following the example of molecule \{V15\}, we give another theoretical molecule model regarding the four 1/2-spins system with total spin S=1 and predict the local moments to be 1/10u_B, 9/10u_B, 1/10u_B,9/10u_B respectively.