标题： 孤立零Chern数平带中的分数Chern绝缘体态 显示英文标题

标题： Fractional Chern insulator states in an isolated flat band of zero Chern number

摘要： 具有零陈数且通过远大于相互作用强度的能隙与希尔伯特空间其余部分良好隔离的平带，在分数量子霍尔物理相关性方面一直未被重视。 在这项工作中，我们展示了一项数值研究，以证明在这种由各向异性跃迁强度的磁通量立方晶格所承载的孤立零陈数平带中，分数量子化绝缘体（FCI）态的出现。尽管在拓扑上是平凡的，这种平带表现出一种引人注目的量子几何特性：量子度规张量迹与贝里曲率之差为常数。 我们考虑最近邻排斥作用足够弱，以确保孤立能带极限始终满足的情况，在此情况下，相互作用引起的能带重正化不会改变平带的量子几何性质，只会引入微小的能带宽度。 在孤立平带的$2/3$填充时，我们的精确对角化计算显示了FCI态明确无误的证据，这些证据来自多体谱和多体陈数，后者展示了$e^2/3h$的分数量化霍尔电导。 而torus上的三重基态简并性表明，带折叠霍尔晶体场景与在$2/3$填充下观测到的$1/3$量化霍尔电导不兼容。 我们发现，即使在孤立能带极限下有限分散作用很小，由于相互作用重整化而获得的有限分散对于FCI的出现是必要的。 随着各向异性趋向于解链极限，FCI经历了一个拓扑相变，转变为链间电荷密度波。 显示英文摘要

摘要： A flat band with zero Chern number, and well isolated from the rest of Hilbert space by a gap much larger than interaction strength, is a context that has not been regarded as relevant for fractional quantum Hall physics. In this work, we present a numerical study to demonstrate the emergence of fractional Chern insulator (FCI) states in such isolated flat band with zero Chern number, which is hosted by a fluxed dice lattice with anisotropic hopping strength. While being topologically trivial, this flat band features an intriguing quantum geometry: the difference between the trace of quantum metric tensor and the Berry curvature is a constant. We consider nearest-neighbor repulsion that is weak enough to ensure that the isolated band limit is always satisfied, where band renormalization by interaction leaves the flat band quantum geometry unchanged and introduce a tiny band width only. At $2/3$ filling of the isolated flat band, our exact diagonalization calculations show unambiguous evidences for the FCI states, both from the many-body spectra and the many-body Chern number that demonstrates a fractionally quantized Hall conductance of $e^2/3h$. And the 3-fold ground state degeneracy on torus suggests that band-folding Hall crystal scenario is not compatible with the observed $1/3$ quantized Hall conductance at $2/3$ filling. We find the finite dispersion acquired from interaction renormalization, albeit tiny in the isolated band limit, is necessary for FCI to emerge. With anisotropy getting stronger towards the disconnected-chains limit, the FCI undergoes a topological phase transition to inter-chain charge density wave.