A new kind of spin-1 chain model with competing dimer and trimer interactions

A new kind of spin-one chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge $c=2$ . A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and Affleck-Kennedy-Lieb-Tasaki models and contain both two- and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a one-to-one resemblance to the phase diagram of the bilinear-biquadratic spin-one chain Hamiltonian, our model is rooted in a very different physical origin, namely, the two competing tendencies of spin-one particles to form singlets through either dimer or trimer formation.A new kind of spin-one chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge $c=2$. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and Affleck-Kennedy-Lieb-Tasaki models and contain both two- and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a one-to-one resemblance to the phase diagram of the bilinear-biquadratic spin-one chain Hamiltonian, our model is rooted in a very different physical origin, namely, the two competing tendencies of spin-one particles to form singlets through either dimer or trimer formation.

arXiv:1709.01344Physical review. B./Physical review. BOct 13, 201710 citations

The ground state of anS= 1/2 distorted diamond chain - a model of Cu3Cl6(H2O)2·2H8C4SO2

Kiyomi Okamoto, Taskashi Tonegawa, Yutaka Takahashi +1 more

We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu 3 Cl 6 (H 2 O) 2 2H 8 C 4 SO 2 in which a non-magnetic ground state was observed recently. This model consists of stacked trimers and has three kinds of coupling constant describing the couplings between spins: the intra-trimer coupling constant J 1 and the inter-trimer coupling constants J 2 and J 3 . All of these constants are assumed to be antiferromagnetic. By use of an analytical method and physical considerations, we show that there are three phases on the 2 - 3 plane ( 2 J 2 / J 1 , 3 J 3 / J 1 ): the dimer phase, the spin-fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists an excitation gap between the twofold-degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu 3 Cl 6 (H 2 O) 2 ·2H 8 C 4 SO 2 . We also obtain the phase diagram on the 2 - 3 plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu 3 Cl 6 (H 2 O) 2 2H 8 C 4 SO 2 in which a non-magnetic ground state was observed recently. This model consists of stacked trimers and has three kinds of coupling constant describing the couplings between spins: the intra-trimer coupling constant J 1 and the inter-trimer coupling constants J 2 and J 3 . All of these constants are assumed to be antiferromagnetic. By use of an analytical method and physical considerations, we show that there are three phases on the 2 - 3 plane ( 2 J 2 / J 1 , 3 J 3 / J 1 ): the dimer phase, the spin-fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists an excitation gap between the twofold-degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu 3 Cl 6 (H 2 O) 2 ·2H 8 C 4 SO 2 . We also obtain the phase diagram on the 2 - 3 plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.

arXiv:cond-mat/9907440Journal of Physics Condensed MatterDec 9, 199966 citations

A novel class of translationally invariant spin chains with long-range interactions

Basur Mallick, B., Federico Finkel, Artemio González-López

Aug 21, 20203 citations

One-Dimensional Quantum Spin-1/2 Chain Models

M. S. Ramkarthik, Pranay Barkataki

CRC Press eBooksSep 22, 20220 citations

c=2

. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and Affleck-Kennedy-Lieb-Tasaki models and contain both two- and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a one-to-one resemblance to the phase diagram of the bilinear-biquadratic spin-one chain Hamiltonian, our model is rooted in a very different physical origin, namely, the two competing tendencies of spin-one particles to form singlets through either dimer or trimer formation.