The spin 1/2 Heisenberg star with frustration II: The influence of the embedding medium

TL;DR

This paper explores how the embedding medium affects the properties of a spin 1/2 Heisenberg star, analyzing eigenvalues, eigenfunctions, and correlations in various lattice configurations and frustration levels.

Contribution

It generalizes the Heisenberg star model by incorporating different embedding media and studies their impact on the system's ground state and thermodynamic properties.

Findings

Eigenvalues and eigenfunctions depend on the embedding medium.

Ground state properties vary with frustration parameter $eta=J_2/J_1$.

Thermodynamic behavior is characterized for Lieb-Mattis antiferromagnetic embedding.

Abstract

We investigate the spin 1/2 Heisenberg star introduced in J. Richter and A. Voigt, J. Phys. A: Math. Gen. {\bf 27}, 1139 (1994). The model is defined by $H=J_1 \sum_{i=1}^{N}{{\bf s}_0{\bf s}_i} + J_2 H_{R}\{{\bf s}_i\}$ ; $J_1,J_2 \ge 0$ , $i=1,...,N$. In extension to the Ref. we consider a more general $H_{R}\{{\bf s}_i\}$ describing the properties of the spins surrounding the central spin ${\bf s}_0$. The Heisenberg star may be considered as an essential structure element of a lattice with frustration (namely a spin embedded in a magnetic matrix $H_R$) or, alternatively, as a magnetic system $ H_R $ with a perturbation by an extra spin. We present some general features of the eigenvalues, the eigenfunctions as well as the spin correlation $\langle {\bf s}_0{\bf s}_i \rangle$ of the model. For $H_R$ being a linear chain, a square lattice or a Lieb-Mattis type system we present the ground state properties of the model in dependence on the frustration parameter $\alpha=J_2/J_1$. Furthermore the thermodynamic properties are calculated for $H_R$ being a Lieb--Mattis antiferromagnet.