标题： 通过耦合到拓扑自旋纹理的Yao-Lee模型中的涌现相 显示英文标题

标题： Emergent phases in the Yao-Lee model via coupling to topological spin textures

摘要： 金属中的电子在与具有非零标量自旋手性的自旋纹理（例如斯格明子）耦合时会经历一个有效的矢量势。 这种耦合可以产生显著的场，导致明显的可观测现象，包括拓扑霍尔效应。 受此启发，我们考虑了一个双层模型，在该模型中，第一层Yao-Lee模型中的马约拉纳费米子通过自旋-自旋相互作用与第二层的拓扑自旋纹理相互作用。 与Kitaev模型不同，Yao-Lee模型仍然完全可解，这使我们可以进行蒙特卡洛模拟以确定其基态。 我们的分析表明，斯格明子晶体可以产生各种各样的vison晶体，这些晶体是由具有诸如Kagome图案等异常模式的$\mathbb{Z}_2$流量组成的周期性排列。 此外，马约拉纳费米子从斯格明子晶体中获得显著的Berry相位，从而导致具有有限Chern数（高达$\nu =5$）的相位。 在磁性层中存在单个斯格明子缺陷的情况下，可以实现相应的vison配置缺陷。 当自旋液体有能隙时，这些缺陷支持局域态。 类似于斯格明子晶体，螺旋自旋纹理也产生了多种流晶。 然而，在这种情况下，大多数这些相都是无能隙的，只有少数是平凡地有能隙的。 我们的结果突显了量子自旋液体中拓扑自旋纹理与分数化准粒子之间相互作用所表现出的丰富物理现象。 显示英文摘要

摘要： Electrons in metals experience an effective vector potential when coupled to spin textures with non-zero scalar spin chirality, such as skyrmions. This coupling can generate a substantial field, leading to pronounced observable phenomena, including the topological Hall effect. Motivated by this, we consider a bilayer model in which the Majorana fermions in the Yao-Lee model on one layer interact with topological spin textures on the second layer via a spin-spin interaction. Unlike the Kitaev model, the Yao-Lee model remains exactly solvable, allowing us to perform Monte Carlo simulations to determine its ground state. Our analysis indicates that skyrmion crystals can give rise to a variety of vison crystals that are periodic arrangements of the $\mathbb{Z}_2$ fluxes with unusual patterns such as a kagome pattern. In addition, Majorana fermions acquire a substantial Berry phase from skyrmion crystals, resulting in phases with finite Chern numbers up to $\nu =5$. In the case of a single skyrmion defect in the magnetic layer, a corresponding defect in the vison configuration can be realized. These defects support localized states when the spin liquid is gapped. Similar to skyrmion crystals, spiral spin textures also give rise to a diverse range of flux crystals. However, in this case, most of these phases are gapless, with only a few being trivially-gapped. Our results highlight the rich physics emerging from the interplay between topological spin textures and fractionalized quasiparticles in quantum spin liquids.