We show that the low-energy sector of the $S=1/2$ , antiferromagnetic Heisenberg model on a one-dimensional lattice of coupled tetrahedra consists of ${2}^{N}$ replica of the spectrum of the dimerized Heisenberg chain, where N is the number of tetrahedra. This provides a proof of the following properties: (i) there is a residual ground-state entropy per spin equal to $(1/4)\mathrm{ln}2$ ; (ii) there is a singlet-triplet gap as long as the coupling between the tetrahedra is smaller than the internal one. These properties are compared to available results on the pyrochlore lattice.We show that the low-energy sector of the $S=1/2$, antiferromagnetic Heisenberg model on a one-dimensional lattice of coupled tetrahedra consists of ${2}^{N}$ replica of the spectrum of the dimerized Heisenberg chain, where N is the number of tetrahedra. This provides a proof of the following properties: (i) there is a residual ground-state entropy per spin equal to $(1/4)\mathrm{ln}2$; (ii) there is a singlet-triplet gap as long as the coupling between the tetrahedra is smaller than the internal one. These properties are compared to available results on the pyrochlore lattice.

arXiv:cond-mat/9812250Physical review. B, Condensed matterJun 1, 199930 citations

Variational Ground-State of the One-Dimensional Heisenberg Model

Jay D. Mancini, Vassilios Fessatidis, Robert K. Murawski +2 more

Bulletin of the American Physical SocietyMar 18, 20090 citations

Ferrimagnetic states inS= 1/2 frustrated Heisenberg chains with period 3 exchange modulation

K Hida

The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization M s . On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than M s /3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization M s . On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than M s /3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.

arXiv:cond-mat/0608582Journal of Physics Condensed MatterMar 23, 200725 citations

We show that the low-energy sector of the

S=1/2

, antiferromagnetic Heisenberg model on a one-dimensional lattice of coupled tetrahedra consists of

{2}^{N}

replica of the spectrum of the dimerized Heisenberg chain, where N is the number of tetrahedra. This provides a proof of the following properties: (i) there is a residual ground-state entropy per spin equal to

(1/4)\mathrm{ln}2

; (ii) there is a singlet-triplet gap as long as the coupling between the tetrahedra is smaller than the internal one. These properties are compared to available results on the pyrochlore lattice.