Unifying Approaches to Novel Quantum Phases in Low-Dimensional Magnets

构造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。多自旋交换相互作用(尤其是环交换相互作用)本身就很耐人寻味，因为这些相互作用被认为是许多奇异量子相的潜水工具。我们确定了呈现新相类型(如交错二聚体、交错标量手性、向列相等)的梯形模型的全局相结构。从基于高度对称性的统一观点来看。我们的分析表明，通过考虑有效的自旋玻色液体(S=1)，可以理解这些体系的基本相结构。我们还利用收缩重整化(CORE)方法将我们的方法扩展到二维情况。这是理解自旋1三角晶格反铁磁体基态相的第一步。在三角形晶格上发现了一种新的自旋为1的二维反铁磁体，这引发了人们对S=1三角形晶格反铁磁体的各种基态相的兴趣。我们剥离了一维子集(锯齿形阶梯)，并结合大规模数值模拟和场论方法研究了相图。研究了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在单重态以上表现出有限的自旋能隙，当施加足够强的电场时，发生自旋玻色-爱因斯坦凝聚(BEC)。根据自旋-BEC的标准理论，观测到的自旋能隙和自旋-BEC质量所在的临界场似乎是不一致的。我们提出了一种新的假设，即BEC发生在自旋五重通道中，以解释该化合物的磁性。这种新的自旋BEC最显着的特点是，即使在磁化开始后，横向磁化也是消失的。

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.