论文标题
在具有短距离相互作用的系统中haldane伪势的出现
Emergence of Haldane pseudo-potentials in systems with short-range interactions
论文作者
论文摘要
在分数量子厅效应的环境中，我们研究了较短的强，反击两体相互作用电位的影响。我们证明，当潜在的范围趋于零，而其强度倾向于无限时，霍尔丹的伪电量运算符（包括其前成分）在数学上是这种相互作用的严格限制。在一种常见的方法中，相互作用电位在最低的兰道水平的角动量特征状态中扩展，这相当于将预成分作为潜力的力矩。这种程序不适合非常强烈的相互作用，尤其是在硬球的情况下。我们在短距离情况下得出有效的公式，该公式涉及在不同角动量通道中而不是其矩中相互作用电位的散射长度。我们的结果适用于玻色子和费米子，并在\ cite {ls}中概括了先前的结果，这些结果适用于最低角动量通道中的玻色子。我们的主要定理在整个希尔伯特空间中以规范性的抗验证意义上的融合，在适当的能量尺度之后，在最低的兰道水平上具有接触相互作用的哈密顿人。
In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane's pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of hard spheres. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our results hold for bosons and fermions alike and generalize previous results in \cite{LS}, which apply to bosons in the lowest angular momentum channel. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level.
