Quantum Phase Transitions in Strongly Correlated Electron Systems

分析了Shastry-Sutherland自旋系统的精确基态和激发谱，以及磁化平台的存在和性质。此外，还研究了该模型中可能出现的量子相变。本文用随机级数展开的方法分析了二维元格RVB系统中杂质效应对量子相变的消除作用，研究了具有二聚、元格和混合自旋结构的SrCu_2（BO_3）_2系统的量子相变：分析了价键固体与各种磁有序相之间的跃迁条件，讨论了SU（4）对称的具有自旋和轨道（同位旋）的Kugel-Khomskii链的低能性质自由度已经从对称性的观点和数值分析研究。基于自旋和轨道自由度的局域化，研究了Ca掺杂Sr_2RuO_4的多轨道效应，计算了Ca掺杂Sr_2RuO_4的基态和低能性质。已经研究了具有自旋-1/2和自旋-1自由度AF的（几何阻挫）烧绿石系统，鉴于由大剩余熵驱动的量子相变，包括Jahn-Teller型形变，在掺杂的Kondo晶格模型中研究了Luttinger液体行为，研究了自旋三重态超导体Sr_2RuO_4的磁关联与非常规超导电性的关系。对非对角无序量子线和耦合链中的能量、准粒子态密度和局域化效应进行了分类。

The exact ground state and the excitation spectrum of the Shastry-Sutherland spin system, and the presence of magnetization plateaus and their properties have been analyzed. Furthermore the possible quantum phase transition within this model has been studied. This problem applies to SrCu_2(BO_3)_2, which is a system close to a quantum critical point.The elimination of the quantum phase transitions due to impurity effects in two-dimensional plaquette RVB systems was analyzed by means of stochastic series expansion.Quantum phase transition in systems with dimerized, plaquette or mixed spin structures : the conditions for the transition between a valence-bond solid and various magnetically ordered plases have been analyzed for various cases.The low-energy properties of the SU(4)-symmetric Kugel-Khomskii chain with spin and orbital (isospin) degrees of freedom have been studied analytically from symmetry point of view and numerically. The multi-orbital effects have been investigated for Ca-doped Sr_2RuO_4 based on localized spin and orbital degrees of freedom which occur in an orbital-dependent Mott-transition.The ground state and low-energy properties of the (geometrically frustrated) pyrochlore systems with spin-1/2 and spin-1 degrees af freedom have been studied, in view of the quantum phase transition driven by large residual entropy, including Jahn-Teller type of deformations.The Luttinger liquid behavior was investigated in the doped Kondo lattice model, where a new small energy scale appears.The relation between magnetic correlation and the unconventional superconductivity was studied for the case of the spin-triplet superconductor Sr_2RuO_4.Properties of the low-energy quasiparticle density of states and localization effects in quantum wires and coupled chains with off-diagonal disorder have been classified.