Exact ground states for coupled spin trimers

Abstract

We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states. The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers $s$ and their ground state $\Phi$ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to $\Phi$ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for $\Phi$ being a ground state. The classical case $s\to \infty$ can be completely analyzed. For the quantum case we consider a couple of examples, where the critical values of the inter-trimer couplings are numerically determined. These examples include chains of corner sharing tetrahedra as well as certain spin tubes. $\Phi$ is proven to be gapped in the case of trimer chains. This follows from a more general theorem on quantum chains with product ground states.

11 figures

References in corpus (10)

• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Magnetic characterization of the frustrated three-leg ladder compound [(CuCl2tachH)3Cl]Cl2
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Quantum phase transitions of the asymmetric three-leg spin tube
• Low-lying excitations of the three-leg spin tube using the density-matrix renormalization group method
• Heat capacity uncovers physics of a frustrated spin tube
• Exact models for trimerization and tetramerization in spin chains
• Gapless points of dimerized quantum spin chains: analytical and numerical studies

Cited by in corpus (11)

• Heisenberg Spin Bus as a Robust Transmission Line for Perfect State Transfer
• Emergent many-body composite excitations of interacting spin-1/2 trimers
• Long-range and short-range magnetic correlations, and microscopic origin of net magnetization in the spin-1 trimer chain compound CaNi3P4O14
• Exact ground states with deconfined gapless excitations for the 3 leg spin-1/2 tube
• Excitations in the spin-1 trimer chain compound CaNi3P4O14: gapped dispersive spinwaves to gapless magnetic excitations
• Magnetization distribution in a spin ladder-shaped quantum nanomagnet
• DMRG studies on linear-exchange quantum spin models in one dimension
• The general spin triangle
• Inelastic Neutron Scattering in Weakly Coupled Triangular Spin Tubes CsCrF${}_4$
• Exact ground state of a frustrated integer-spin modified Shastry-Sutherland model
• Covariance-based method for eigenstate factorization and generalized singlets