论文标题
霍夫斯塔特蝴蝶的分数披露费用和离散转移
Fractional disclination charge and discrete shift in the Hofstadter butterfly
论文作者
论文摘要
在存在晶体对称性的情况下，物质的拓扑阶段获得了许多不变的寄主，导致非平凡的量化响应。在这里，我们研究了一个特定的不变，离散的移位$ \ mathscr {s} $，适用于Free Fermions的Square Grattice Hofstadter模型。 $ \ mathscr {s} $与$ \ mathbb {z} _m $ $分类在$ m $ - 折叠的旋转对称性和电荷保护的情况下相关联。 $ \ mathscr {s} $对（i）与晶格披露结合的分数电荷给出了量化的贡献，以及（ii）基态的角动量，并具有附加的，对称的磁性通量。 $ \ mathscr {s} $形成了自己的“ hofstadter Butterfly”，我们在数字上计算，并完善了霍夫斯塔特模型的通常相位图。我们为hofstadter频段的密度和通量，为$ \ mathscr {s} $提出了一个经验公式，我们得出了许多一般约束。我们表明，具有相同Chern号码的频段可能具有$ \ Mathscr {s} $的不同值，尽管奇怪的甚至Chern编号频段始终具有$ \ Mathscr {S} $的一半和整数值。
In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to non-trivial quantized responses. Here we study a particular invariant, the discrete shift $\mathscr{S}$, for the square lattice Hofstadter model of free fermions. $\mathscr{S}$ is associated with a $\mathbb{Z}_M$ classification in the presence of $M$-fold rotational symmetry and charge conservation. $\mathscr{S}$ gives quantized contributions to (i) the fractional charge bound to a lattice disclination, and (ii) the angular momentum of the ground state with an additional, symmetrically inserted magnetic flux. $\mathscr{S}$ forms its own `Hofstadter butterfly', which we numerically compute, refining the usual phase diagram of the Hofstadter model. We propose an empirical formula for $\mathscr{S}$ in terms of density and flux per plaquette for the Hofstadter bands, and we derive a number of general constraints. We show that bands with the same Chern number may have different values of $\mathscr{S}$, although odd and even Chern number bands always have half-integer and integer values of $\mathscr{S}$ respectively.
