标题： 用四元数在分数量子霍尔效应中解锁新的规范 显示英文标题

标题： Unlocking new regimes in fractional quantum Hall effect with quaternions

摘要： 我们证明，将分数量子霍尔（FQH）效应的复合费米子理论用四元数来表述，大大扩展了它的适用范围，并打开了许多以前无法进行定量理论研究的有趣问题的大门。 作为例证，我们通过寻找磁旋波不稳定性，研究了在半填充的朗道能级和附近FQH态中，复合费米子费米海可能出现的向列相或电荷密度波不稳定性。 我们对FQH效应的四元数表述受到在引力波模式和宇宙微波背景辐射的理论分析中的数学发展所启发，在这些分析中，自旋加权球谐函数起着重要作用，而它们只不过是出现在FQH效应球几何中的单极谐波。 显示英文摘要

摘要： We demonstrate that formulating the composite-fermion theory of the fractional quantum Hall (FQH) effect in terms of quaternions greatly expands its reach and opens the door into many interesting issues that were previously beyond the reach of quantitative theoretical investigation. As an illustration, we investigate the possibility of a nematic or a charge-density wave instability of the composite-fermion Fermi sea at half-filled Landau level and of the nearby FQH states by looking for a magneto-roton instability. Our quaternion formulation of the FQH effect has been inspired by mathematical developments in the theoretical analyses of gravitational wave modes and cosmic microwave background radiation, where an important role is played by spin-weighted spherical harmonics which are nothing but monopole harmonics appearing in the spherical geometry for the FQH effect.