具有硬壁势的环形分数量子霍尔液体
Ring-shaped fractional quantum Hall liquids with hard-wall potentials
摘要：
我们研究了$ν=1/2$玻色子分数量子霍尔液滴的物理性质。试验波函数的基础上扩展的杰克多项式形式主义，包括两个不同的手征边缘提出并验证了广泛的限制潜力，其出色的重叠与本征态数值精确对角化。在中心位于原点的单个排斥势的存在下，发现了多体光谱中的递归结构和大量简并的基态流形.通过加入第二个硬壁势从外部限制分数量子Hall液滴，得到了一个非简并的基态，其中在中心处含有一定数量的准空穴，对于合适的势参数，两个边缘上的激励的清晰组织。鉴于分数量子霍尔物理学的微妙方面的理论和实验研究，这种环形配置的效用概述。
英文摘要：
We study the physics of $ν=1/2$ bosonic fractional quantum Hall droplets confined in a ring-shaped region delimited by two concentric cylindrically symmetric hard-wall potentials. Trial wave functions based on an extension of the Jack polynomial formalism including two different chiral edges are proposed and validated for a wide range of confinement potentials in terms of their excellent overlap with the eigenstates numerically found by exact diagonalization. In the presence of a single repulsive potential centered in the origin, a recursive structure in the many-body spectra and a massively degenerate ground state manifold are found. The addition of a second hard-wall potential confining the fractional quantum Hall droplet from the outside leads to a non-degenerate ground state containing a well defined number of quasiholes at the center and, for suitable potential parameters, to a clear organization of the excitations on the two edges. The utility of this ring-shaped configuration in view of theoretical and experimental studies of subtle aspects of fractional quantum Hall physics is outlined.
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