Unifying Approaches to Novel Quantum Phases in Low-Dimensional Magnets

包含多自旋交换相互作用的一维和二维量子磁体中竞争序的统一理论的构建。多自旋交换相互作用（特别是环交换相互作用）的效应本身就很有趣，因为这些相互作用被认为是许多奇异量子相的潜水锄头。我们确定了梯型模型的全局相结构，这些模型表现出新的相类型（如交错二聚体，交错标量手征，等）。基于高度对称性的统一观点。我们的分析表明，这些系统的基本相结构可以理解，通过考虑有效玻色液体的自旋（S=1）。我们还利用收缩重整化（CORE）方法将我们的方法推广到二维情形，为理解自旋为1的三角晶格反铁磁体的基态相位迈出了第一步.三角晶格上自旋为1的二维反铁磁体的发现引发了人们对S=1三角晶格反铁磁体中各种基态相的兴趣。我们剥离出一维的梯形子组，并结合大规模数值模拟和场论方法研究了其相图。一种新的二维自旋带隙化合物（CuCl）LaNb_2O_7的磁性。铜基化合物（CuCl）LaNb_2O_7在单重态基态上具有有限的自旋能隙，在强电场作用下发生自旋玻色爱因斯坦凝聚（BEC）。根据自旋BEC的标准理论，所观测到的自旋能隙与自旋BEC质量所处的临界场似乎是不一致的。我们提出了一个新的设想，即BEC发生在自旋五重态通道中，以解释该化合物的磁性。这种新的自旋BEC最显著的特点是，即使在磁化开始后，横向磁化也消失了。

Construction of unifying theories for competing orders in one- and two dimensional quantum magnets which contain multi-spin exchange interactions. The effect of multi-spin exchange interactions (ring-exchange interaction, in particular) is intriguing in its own right since these interactions are thought of as diving hoes of many exotic quantum phases. We determined the global phase structures of ladder-type models which exhibit new kinds of phases (e.g. staggered dimer, staggered scalar chiral, nematic, etc.) from a unifying viewpoint based on high symmetries. Our analysis shows that the basic phase structure of these systems can be understood by considering effective Bose liquids with spins (S=1). We also extended our methods to two-dimensional cases by using the contractor-renormalization (CORE) method.A first step toward the understanding of the ground-state phases of spin-1 triangular lattice antiferromagnets. The discovery of a new spin-1 two-dimensional antiferromagnet on a triangular lattice sparked interests on various ground-state phases in S=1 triangular-lattice antiferromagnets. We stripped off a one-dimensional subset (zigzag ladder) and investigated the phase diagram by a combined use of large-scale numerical simulations and field-theoretical methods.Magnetism of a new two-dimensional spin-gap compound (CuCl)LaNb_2O_7. The Cu-based compound (CuCl)LaNb_2O_7 exhibits a finite spin gap above a singlet ground state and undergoes a spin-Bose-Einstein condensation (BEC) when strong enough field is applied. According to the standard theory of spin-BEC, the observed spin gap and the critical field, at which spin-BEC mass, seem inconsistent with each other. We proposed a new scenario that BEC occurs in spin-quintet channel to explain magnetism of this compound. The most remarkable feature of this new kind of spin-BEC is that the transverse magnetization vanishes even after the onset of magnetization.