Exact ground state and elementary excitations of the spin tetrahedron chain

Chen, Shu; Wang, Yupeng; Ning, Wei; Wu, Congjun; Lin, Hai–Qing

doi:10.1103/physrevb.74.174424

Cited by 12 publications

(8 citation statements)

References 36 publications

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“…A possible way to realize such a system experimentally is described in Appendix A. Moreover, it has been suggested recently that an SU(3) trimer state might be realized approximately in a spin tetrahedron chain [61,62].…”

Section: Introductionmentioning

confidence: 99%

Valence bond solids forSU(n)spin chains: Exact models, spinon confinement, and the Haldane gap

2007

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To begin with, we introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation3 of SU (3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and hence a Haldane gap in the excitation spectrum. We generalize some of our models to SU(n). Finally, we use the emerging rules for the construction of VBS states to argue that models of antiferromagnetic chains of SU(n) spins in general possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes λ which is divisible by n. If λ and n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λ and n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.

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Section: Introductionmentioning

confidence: 99%

Valence bond solids forSU(n)spin chains: Exact models, spinon confinement, and the Haldane gap

2007

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“…Recently, theoretical investigation of strongly geometrical frustration materials [10] have been performed, particularly focused on the diamond chain structure, using several numerical approaches [11,12]. These theoretical results could enhance the other experimental realizations provided by the polymeric compounds such as Cu2OSO4 [13] and M3(OH)2 (with M=Ni, Co, Mn) [14,15].…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of the asymmetric tetrahedral Ising–Heisenberg chain

Valverde

Rojas

Souza

2008

J. Phys.: Condens. Matter

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The asymmetric tetrahedron is composed by all edges of tetrahedron represented by Ising interaction except one, which has a Heisenberg type interaction. This asymmetric tetrahedron is arranged connecting a vertex which edges are only Ising type interaction to another vertex with same structure of another tetrahedron. The process is replicated and this kind of lattice we call the asymmetric Ising-Heisenberg chain. We have studied the ground state phase diagram for this kind of models. Particularly we consider two situations in the Heisenberg-type interaction, (i) The asymmetric tetrahedral spin(1/2,1/2) Ising-XYZ chain, and (ii) the asymmetric tetrahedral spin-(1/2,1) Ising-XXZ chain, where we have found a rich phase diagram and a number of multicritical points. Additionally we have also studied their thermodynamics properties and the correlation function, using the decorated transformation. We have mapped the asymmetric tetrahedral Ising-Heisenberg chain in an effective Ising chain, and we have also concluded that it is possible to evaluate the partition function including a longitudinal external magnetic field.

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“…In addition to the ideal DDC as defined in Eq. ͑1͒, models with somewhat modified interactions, such as the tetrahedron chain 12 and the strongly anisotropic xy version of the DDC, 13 have been considered and serve to illustrate the effect of deviating from the ideal isotropic diamond structure.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a distorted diamond chain

Mikeska

Luckmann

2008

Phys. Rev. B

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We present results on the dynamics of the distorted diamond chain, S =1/ 2 dimers alternating with single spins 1 / 2 and exchange couplings J 1 and J 3 in between. The dynamics in the spin fluid ͑SF͒ and tetramerdimer ͑TD͒ phases is investigated numerically by exact diagonalization for up to 24 spins. Representative excitation spectra are presented both for zero magnetic field and in the 1 / 3 plateau phase and the relevant parameters are determined across the phase diagram. The behavior across the SF-TD phase transition line is discussed for the specific heat and for excitation spectra. The relevance of the distorted diamond chain model for the Cu 3 ͑CO 3 ͒ 2 ͑OH͒ 2 ͑azurite͒ material is discussed with particular emphasis on inelastic neutron scattering experiments; the recent suggestion of one possibly ferromagnetic coupling constant is not confirmed.

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Exact ground state and elementary excitations of the spin tetrahedron chain

Cited by 12 publications

References 36 publications

Valence bond solids forSU(n)spin chains: Exact models, spinon confinement, and the Haldane gap

Valence bond solids forSU(n)spin chains: Exact models, spinon confinement, and the Haldane gap

Phase diagram of the asymmetric tetrahedral Ising–Heisenberg chain

Dynamics of a distorted diamond chain

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