论文标题
沮丧的量子磁性的物质拓扑状态
Topological States of Matter in Frustrated Quantum Magnetism
论文作者
论文摘要
沮丧的量子磁铁可能表现出迷人的集体现象。本文的主要目的是为物质的新阶段（如局部量子自旋模型中的量子自旋液体）出现提供结论性证据。我们开发了用于大规模精确对角度计算的新型算法。提出了有效使用晶格对称性的sublattice编码方法，在对角度化汉密尔顿矩阵的过程中，提出了一种随机分布的记忆并行化策略。已经执行了系统尺寸的各种超级计算机上的计算基准测试。提出了有关沮丧的Kagome Heisenberg Antiferromagnet中手性旋转液体出现的结果。讨论了此阶段的稳定性和程度。在三角形晶格上的海森堡模型中，我们建立了另一个手性旋转液相。我们讨论了Heisenberg $ J_1 $ - $ J_2 $型号的特殊情况，并提出了一种场景，其中从120度néel到推定的$ \ Mathbf {Z} _2 _2 $旋转液体的临界点的关键点是由Dirac Spin液体描述的。讨论了带有SU（N）在三角形晶格上具有SU（N）自由度的Heisenberg模型的概括，并讨论了附加的环形交换项。我们介绍了对项目的贡献和最终结果，这些结果表明在扩展参数范围内进行了一系列手性旋转液相。最后，我们介绍了从n = 2，...，10和多柱表示的正方形晶格上的SU（N）版本的量子蒙特卡洛研究中的初步数据。我们建立了Néel有序相位与无序相之间的相边界。预计四柱表示中的无序相将是Spin-1 Heisenberg链的Haldane相的二维类似物。
Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin models. We develop novel algorithms for large-scale Exact Diagonalization computations. Sublattice coding methods for efficient use of lattice symmetries in the procedure of diagonalizing the Hamiltonian matrix are proposed and suggest a randomized distributed memory parallelization strategy. Benchmarks of computations on various supercomputers with system size up to 50 spin-1/2 particles have been performed. Results concerning the emergence of a chiral spin liquid in a frustrated kagome Heisenberg antiferromagnet are presented. The stability and extent of this phase are discussed. In an extended Heisenberg model on the triangular lattice, we establish another chiral spin liquid phase. We discuss the special case of the Heisenberg $J_1$-$J_2$ model and present a scenario where the critical point of phase transition from the 120-degree Néel to a putative $\mathbf{Z}_2$ spin liquid is described by a Dirac spin liquid. A generalization of the SU(2) Heisenberg model with SU(N) degrees of freedom on the triangular lattice with an additional ring-exchange term is discussed. We present our contribution to the project and the final results that suggest a series of chiral spin liquid phases in an extended parameter range. Finally, we present preliminary data from a Quantum Monte Carlo study of an SU(N) version of the J-Q model on a square lattice for N=2,...,10, and multi-column representations. We establish the phase boundary between the Néel ordered phase and the disordered phases. The disordered phase in the four-column representation is expected to be a two-dimensional analog of the Haldane phase for the spin-1 Heisenberg chain.
