Theoretical Study on Quantum Phase Transitions by the Density Matrix Renormalization Group Method

Yb_4As_3是一个近藤系统，载流子密度很小。然而，Fulde教授及其同事提出，由电荷有序形成的一维自旋链是T中比热线性的原因。Kohgi教授小组的中子散射测量证实了这一提议。然而，在磁场中打开间隙的现象仍然是一个悬而未决的问题。我们分析了Yb_4As_3的结构，指出Dzyaloshinskii-Moriya相互作用是形成自旋能隙的原因。进一步导出了自然包含Dzyaloshinskiii-Moriya相互作用的自旋链的有效哈密顿量。系统的低能有效理论是Sine-Gordon场论。然而，为了理解整个能量范围内的物理，密度矩阵重整化群是最可靠的方法，并且在这一方向上的研究正在进行中.对于在SrCu_2（BO_3）_2中实现的正交二聚体系统，用微扰方法研究了两个三重态激发。已经表明，由于两个三重态激发，较高三重态分支的色散比最低三重态分支的色散更宽。

Yb_4As_3 had been known as a Kondo system with small density of carriers. However, Prof. Fulde and coworkers proposed that the one-dimensional spin chains formed by the charge ordering is responsible for the specific heat linear in T.This proposal was confirmed by the neutron scattering measurements by Prof. Kohgi's group. However, still the phenomena of opening of a gap in magnetic fields remained as an open question. We analyzed the structure of Yb_4As_3 and pointed out that the Dzyaloshinskii-Moriya interaction is responsible for the formation of the spin gap. Further we derived the effective Hamiltonian for the spin chains which naturally contains the Dzyaloshinskii-Moriya interaction. The low energy effective theory for the system is the Sine-Gordon field theory. However, in order to understand the physics in the entire energy range, the density matrix renormalization group is the most reliable method and investigations under this direction is now under way.Concerning the orthogonal dimer system realized in SrCu_2(BO_3)_2, two triplet excitations were investigated by using a perturbative approach. It has been shown that the dispersion for the higher triplet branch due to the two-triplet excitations has a wider dispersion than the lowest one.