标题： Kitaev 双层和摩尔超晶格中的精确可解自旋液体 显示英文标题

标题： Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices

摘要： 基于近年来关于莫尔超晶格的最新进展，我们提出了一种在双层六角格子上具有Kitaev型相互作用的可解析模型，适用于AA堆叠和莫尔超晶格。 通过蒙特卡洛模拟和变分分析，我们揭示了丰富的相态，在基态中，层内和层间的$\mathbb{Z}_2$通量（vison）以周期性的方式排列，由层间耦合和垂直外加磁场调控。 我们进一步将该模型扩展到具有多种公度扭转角度的莫尔超晶格，这些角度围绕六角格子中的两个不同的扭转中心，分别由$C_{3z}$和$C_{6z}$表示。 我们的模拟揭示了与莫尔单位胞内的AA或AB堆叠区域相关的面片值的广义模式。 此外，根据扭转角度、扭转中心和层间耦合强度，莫尔超晶格表现出各种有能隙和无能隙的自旋液体相，并且还可以承载角模和边模。 我们的研究结果强调了精确可解量子自旋液体的双层和扭转双层模型中丰富的物理现象。 显示英文摘要

摘要： Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Employing Monte Carlo simulations and variational analysis, we uncover a rich variety of phases where the intra and interlayer $\mathbb{Z}_2$ fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by $C_{3z}$ and $C_{6z}$ of the honeycomb lattice. Our simulations reveal generalized patterns of plaquette values correlated with the AA or AB stacking regions across the moir\'e unit cell. In addition, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.