We investigate the spin- Heisenberg star introduced by Richter and Voigt. The model is defined by ; , . In extension to the work of Richter and Voigt we consider a more general describing the properties of the spins surrounding the central spin . The Heisenberg star may be considered as an essential structure element of a lattice with frustration (namely a spin embedded in a magnetic matrix ) or, alternatively, as a magnetic system with a perturbation by an extra spin. We present some general features of the eigenvalues, the eigenfunctions as well as the spin correlation of the model. For 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 . Furthermore, the thermodynamic properties are calculated for being a Lieb - Mattis antiferromagnet.We investigate the spin- Heisenberg star introduced by Richter and Voigt. The model is defined by ; , . In extension to the work of Richter and Voigt we consider a more general describing the properties of the spins surrounding the central spin . The Heisenberg star may be considered as an essential structure element of a lattice with frustration (namely a spin embedded in a magnetic matrix ) or, alternatively, as a magnetic system with a perturbation by an extra spin. We present some general features of the eigenvalues, the eigenfunctions as well as the spin correlation of the model. For 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 . Furthermore, the thermodynamic properties are calculated for being a Lieb - Mattis antiferromagnet.

arXiv:cond-mat/9511109Journal of Physics A Mathematical and GeneralFeb 21, 199614 citations

The spin- 1/2 Heisenberg star with frustration: numerical versus exact results

Johannes Richter, A Voigt

We study a spin- 1/2 Heisenberg model H=J 1 Sigma i=2 N S 1 S i +J 2 Sigma i=2 N S i S i+1 ; J 1 , J 2 >or=0 (Heisenberg star) which may be considered either as an essential structure element of a lattice with frustration or, alternatively, as an antiferromagnetic linear chain with a perturbation. We discuss general relations for the energy eigenvalues, the eigenstates as well as the spin correlation of the system in dependence on J 2 /J 1 . The correlation function (S 1 S i ) scales with 1/Z, where Z =N-1 is the number of nearest neighbours i of the central spin 1. In the mean-field limit (Z to infinity ) (S 1 S i ) goes to -0.25 for small J 2 /J 1 , but vanishes for strong frustration J 2 /J 1 . Adding exact numerical results for N=5, 7, ..., 23 we discuss the ground-state phase diagram, in particular, the ground-state spin correlations versus J 2 /J 1 . Analysing the spin correlation of frustrated and non-frustrated stars we suggest an upper bound -0.25 for the ground-state correlator (S i S j )0 of two antiferromagnetically interacting spins i and j in a non-frustrated Heisenberg spin- 1/2 antiferromagnet. We argue that any measured nearest-neighbour spin correlation (S i S j )0 larger than this bound indicates of frustration in quantum spin Heisenberg antiferromagnets.We study a spin- 1/2 Heisenberg model H=J 1 Sigma i=2 N S 1 S i +J 2 Sigma i=2 N S i S i+1 ; J 1 , J 2 >or=0 (Heisenberg star) which may be considered either as an essential structure element of a lattice with frustration or, alternatively, as an antiferromagnetic linear chain with a perturbation. We discuss general relations for the energy eigenvalues, the eigenstates as well as the spin correlation of the system in dependence on J 2 /J 1 . The correlation function (S 1 S i ) scales with 1/Z, where Z =N-1 is the number of nearest neighbours i of the central spin 1. In the mean-field limit (Z to infinity ) (S 1 S i ) goes to -0.25 for small J 2 /J 1 , but vanishes for strong frustration J 2 /J 1 . Adding exact numerical results for N=5, 7, ..., 23 we discuss the ground-state phase diagram, in particular, the ground-state spin correlations versus J 2 /J 1 . Analysing the spin correlation of frustrated and non-frustrated stars we suggest an upper bound -0.25 for the ground-state correlator (S i S j )0 of two antiferromagnetically interacting spins i and j in a non-frustrated Heisenberg spin- 1/2 antiferromagnet. We argue that any measured nearest-neighbour spin correlation (S i S j )0 larger than this bound indicates of frustration in quantum spin Heisenberg antiferromagnets.

Journal of Physics A Mathematical and GeneralFeb 21, 199428 citations

Ground-State Properties of the Frustrated One-Dimensional S=1 Heisenberg Model

Takashi Tonegawa, Makoto Kaburagi, Noriya Ichikawa +1 more

Springer proceedings in physicsJan 1, 19920 citations

Emergent spin-1 trimerized valence bond crystal in the spin- 12 Heisenberg model on the star lattice

Shi-Ju Ran, Wei Li, Shou-Shu Gong +3 more

We explore the frustrated spin- $\frac{1}{2}$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) intertriangle couplings ( ${J}_{e}<0$ ), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening ${J}_{e}$ , the system exhibits a universal scaling behavior either with or without a magnetic field $h$ : the order parameter, the five critical fields that separate the ${J}_{e}\text{\ensuremath{-}}h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on ${J}_{e}$ . Our work implies that the spin-1 VBCs can be stabilized by introducing small FM couplings in the geometrically frustrated spin- $\frac{1}{2}$ systems.We explore the frustrated spin-$\frac{1}{2}$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) intertriangle couplings (${J}_{e}<0$), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening ${J}_{e}$, the system exhibits a universal scaling behavior either with or without a magnetic field $h$: the order parameter, the five critical fields that separate the ${J}_{e}\text{\ensuremath{-}}h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on ${J}_{e}$. Our work implies that the spin-1 VBCs can be stabilized by introducing small FM couplings in the geometrically frustrated spin-$\frac{1}{2}$ systems.

arXiv:1508.03451Physical review. B./Physical review. BFeb 26, 201823 citations

We explore the frustrated spin-

\frac{1}{2}

Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) intertriangle couplings (

{J}_{e}<0

), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening

{J}_{e}

, the system exhibits a universal scaling behavior either with or without a magnetic field

h

: the order parameter, the five critical fields that separate the ${J}_{e}\text{\ensuremath{-}}h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on

{J}_{e}

. Our work implies that the spin-1 VBCs can be stabilized by introducing small FM couplings in the geometrically frustrated spin-

\frac{1}{2}

systems.