Exact models for trimerization and tetramerization in spin chains

Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain

Recent theoretical studies raised the possibility of a realization of spin nematic states in the S=1 triangular lattice compound NiGa_2S_4. We study the bilinear-biquadratic spin 1 chain in a zig-zag geometry by means of the density matrix renormalization group method and exact diagonalization. We present the phase diagram focusing on antiferromagnetic interactions. Adjacent to the known Haldane-double Haldane and the extended critical phase with dominant spin nematic correlations we find a trimerized phase with a nonvanishing energy gap. We discuss results for different order parameters, ener…

Exact trimer ground states on a spin-1 chain

We construct a new spin-1 model on a chain. Its ground state is determined exactly which is three-fold degenerate by breaking translational invariance. Thus we have trimerization. Excited states cannot be obtained exactly, but we determine a few low-lying ones by using trial states, among them solitons.

自旋-3/2 广义海森堡链中的非均匀四极序

Nonuniform quadrupolar orders in the spin-3/2 generalized Heisenberg chain

该研究通过大规模DMRG数值模拟，在自旋-3/2广义海森堡链中发现了非均匀四极序的四聚化相和条纹-Q相，并证明了DM-LL转变点处存在k=1的WZW模型。

Magnetization plateau and quantum phase transition of the S=1/2 trimerized XXZ spin chain

We study the plateau of the magnetization curve at $M = M_{\rm s}/3$ ($M_{\rm s}$ is the saturation magnetization) of the $S=1/2$ trimerized $XXZ$ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the $Δ-t$ plane, where $Δ$ denotes the $XXZ$ anisotropy and $t$ the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.

Quantum Phase Transition of S=1/2 Trimerized XXZ Spin Chain in Magnetic Field

We study the magnetization plateau at a third of the saturation magnetization of the S=1/2 trimerized XXZ spin chain at T=0. The appearance of the plateau depends on the values of the XXZ anisotropy and the magnitude of the trimerization. This plateauful-plateauless transition is a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type, which is difficult to precisely detect from the numerical data. To determine the phase boundary line of this transition precisely, we use the level crossing of low-lying excitations obtained from the numerical diagonalization. We also discuss the …