莫比乌斯分子与脆性莫特绝缘体
Möbius molecules and fragile Mott insulators
摘要：
受有机化学中莫比乌斯芳烃概念的启发，我们将最近引入的脆性莫特绝缘体（FMI）的概念扩展到具有半量子磁通量（$hc/2e$）的排斥哈伯德相互作用的环形分子。在这种情况下，FMI是有限尺寸分子的绝缘基态，其不能与单个斯莱特行列式电连接，即，带绝缘体，只要时间反演和晶格平移对称性被保留。基于有限Hubbard相互作用强度$U$的精确数值对角化和已有的一维Hubbard模型在大$U$极限下的Bethe-Answer研究，我们建立了具有$4n$和$4n+2$位置的Hubbard分子之间的对偶，其中$n$为$n$整数.具有$4n$位点的分子在没有通量的情况下是FMI，但在存在半量子通量的情况下变成能带绝缘体，而具有$4n+2$位点的分子在没有通量的情况下是能带绝缘体，但在存在半量子通量的情况下变成FMI。包括次近邻跳跃产生新的FMI状态，属于多维不可约表示的分子点群，产生丰富的相图。
英文摘要：
Motivated by the concept of Möbius aromatics in organic chemistry, we extend the recently introduced concept of fragile Mott insulators (FMI) to ring-shaped molecules with repulsive Hubbard interactions threaded by a half-quantum of magnetic flux ($hc/2e$). In this context, a FMI is the insulating ground state of a finite-size molecule that cannot be adiabatically connected to a single Slater determinant, i.e., to a band insulator, provided that time-reversal and lattice translation symmetries are preserved. Based on exact numerical diagonalization for finite Hubbard interaction strength $U$ and existing Bethe-ansatz studies of the one-dimensional Hubbard model in the large-$U$ limit, we establish a duality between Hubbard molecules with $4n$ and $4n+2$ sites, with $n$ integer. A molecule with $4n$ sites is an FMI in the absence of flux but becomes a band insulator in the presence of a half-quantum of flux, while a molecule with $4n+2$ sites is a band insulator in the absence of flux but becomes an FMI in the presence of a half-quantum of flux. Including next-nearest-neighbor-hoppings gives rise to new FMI states that belong to multidimensional irreducible representations of the molecular point group, giving rise to a rich phase diagram.
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