量子自旋液体中拓扑拟粒子的性质：量子蒙特卡罗和新的large-N理论

量子自旋液体（QSL）是源于阻挫与强量子涨落的新奇物态，其准粒子（自旋子）有望服从分数统计、用于拓扑量子计算。为此，从理论上深入理解近期在可出现QSL的材料中所观察到的新奇效应极为重要。这些材料的磁激发谱显示出一些反常特征峰，暗示着源于QSL近邻效应的磁子分数化。申请人将运用与合作者近年来开发的理论方法来研究具有稳定QSL的正则哈密顿函数系统，揭示实验发现的物理机理。一方面，利用拓展世界线量子蒙特卡洛方法，结合随机解析延拓，研究量子自旋冰双磁单极的动力学响应，探索量子自旋冰与Z2自旋液体间的新奇拓扑相变。另一方面，利用large-N新理论，把磁子表示成两自旋子的束缚态，计算扩充Kitaev模型磁有序基态的动力学自旋结构因子，通过比较不同初始值的谱线与实验结果，确立上述激发谱分数化的机理。本项目预期对QSL准粒子动力学特性研究带来重要的新结果，为以动力学实验研究探寻QSL提供重要的新线索。

Quantum spin liquids are novel states of matter without long-range order, emerging from frustration and quantum fluctuation. Their quasiparticles (spinons) carry a fractional quantum number and could be a key to achieve topological quantum computing. Towards this goal, it is of fundamental importance to provide a solid understanding of recent experiments in putative model materials, where excitation spectra exhibit anomalous features suggesting fractionalization of magnons, possibly due to proximity effects. To clarify their origins, the applicant will apply new theoretical methods, developed by himself and coworkers, to the canonical Hamiltonians stabilizing spin liquids. Firstly, by using the new large-N theory, which describes magnons as two-spinon bound states, the applicant will evaluate dynamical spin structure factor in magnetically ordered states of the extended Kitaev model. By adopting different ansatz and comparing the spectra against experiments, the origin of fractionalized excitations will be clarified. Secondly, by using the extended world-line quantum Monte Carlo method, combined with the stochastic analytic continuation, the applicant will evaluate response functions of dual (or “electric”, arising from quantum fluctuations in the spin ice manifold in the pyrochlore lattice) monopoles in quantum spin ice. Furthermore, a novel topological phase transition between quantum spin ice and Z2 spin liquid will be investigated by including multi-spin interactions into the model. The obtained insights will shed new lights on dynamics of quasiparticles of spin liquids and provide an invaluable clue for searching for a genuine experimental realization of a spin liquid.