标题： 大$N$相互作用费米子的分数霍尔物理 显示英文标题

标题： Fractional Hall physics from large $N$ interacting fermions

摘要： 我们求解了在最低朗道能级中具有$U(N)$无关相互作用的$N$种费米子模型，在$N\gg 1$极限下。 我们在固定化学势下找到了第二量子化路径积分的鞍点，对应于填充因子为$ \frac{p}{q}$的分数霍尔态，其中整数$p$和$q$取决于化学势和相互作用。 在长环面上有$q$种这样的态，由平移对称性相关联，并且有$SU(N)$-不变的分数电荷激发。值得注意的是，这些鞍点及其填充在$N=1$处作为第二量子化作用量的极值仍然存在。我们的构造从强相互作用费米子出发，给出了分数霍尔态的第一性原理推导。 显示英文摘要

摘要： We solve models of $N$ species of fermions in the lowest Landau level with $U(N)$-invariant interactions in the $N\gg 1$ limit. We find saddles of the second quantized path integral at fixed chemical potential corresponding to fractional Hall states with filling $ \frac{p}{q}$ where the integers $p$ and $q$ depend on the chemical potential and interactions. On a long torus there are $q$ such states related by translation symmetry, and $SU(N)$-invariant excitations of fractional charge. Remarkably, these saddles and their filling persist as extrema of the second-quantized action at $N=1$. Our construction gives a first-principles derivation of fractional Hall states from strongly interacting fermions.