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及其性质。此外，还研究了该模型中可能发生的量子相变。这个问题适用于接近量子临界点的系统--SrCu2(BO_3)_2。用随机级数展开的方法分析了二维板状RVB系统中杂质效应引起的量子相变的消除。分析了二聚化、板状和混合自旋结构体系的量子相变：分析了价键固体和各种磁性有序相之间的相变条件。从对称性的角度和数值方法研究了具有自旋和轨道(同位旋)自由度的SU(4)对称Kugel-Khomskii链的低能性质。基于轨道相关的Mott跃迁中的局域自旋和轨道自由度，研究了掺Ca的Sr2RuO4的多轨道效应.考虑到大的剩余熵驱动的量子相变，包括Jahn-Teller类型的形变，研究了具有自旋-1/2和自旋-1自由度的焦绿石(几何受挫)系统的基态和低能性质.在掺杂的Kondo晶格模型中研究了Luttinger液体行为.以自旋三重态超导体Sr2RuO4为例，研究了磁关联与非常规超导电性的关系。对非对角线无序量子线和耦合链的低能准粒子态密度和局域效应的性质进行了分类。

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.