Half赝势零模研究的代数方法
Algebraic approach to the study of zero modes of Haldane pseudopotentials
摘要：
我们考虑格点哈密顿量，产生于把Haldron赝势成第二个量化或“引导中心唯一”的形式。这些都是无阻挫格点哈密顿的有趣例子。这是因为即使它们的最高密度零能量基态，劳克林态，已知具有矩阵乘积结构（具有无界键维数），这些晶格哈密顿量的无阻挫特征似乎是模糊的，{ \em，除非}人们回到解析最低朗道能级波函数的原始第一量化图像。这一步涉及放回与动力学动量相关的额外自由度，人们想知道这些自由度的增加是否真的有必要认识到基础晶格哈密顿量的无阻挫特性。从根本上说，这些自由度与“仅引导中心”哈密顿量的谱无关。此外，这样的结构是不熟悉的，在研究更简单的（有限范围）挫折自由格点哈密顿量与矩阵乘积基态（有限键维）。零模式的性质的“晶格版本”的赝势可以理解从多项式的自由，本质上晶格的观点也建议的事实，这些赝势是从一个代数构造的合理简单的期待运营商。在这里，我们表明，零模式的属性，因此挫折免费字符，这些晶格哈密顿可以理解为代数结构的后果，这些运营商的一部分。我们相信，我们的研究结果将加深对具有无限键维的矩阵乘积态的父哈密顿量的了解，特别是在分数Chern绝缘体的研究中，可能是有用的。
英文摘要：
We consider lattice Hamiltonians that arise from putting Haldane pseudopotentials into a second quantized or "guiding-center-only" form. These are fascinating examples for frustration free lattice Hamiltonians. This is so since even though their highest density zero energy ground states, the Laughlin states, are known to have matrix-product structure (with unbounded bond dimension), the frustration free character of these lattice Hamiltonians seems obscure, {\em unless} one goes back to the original first quantized picture of analytic lowest Landau level wave functions. This step involves putting back additional degrees of freedom associated with dynamical momenta, and one wonders whether the addition of these degrees of freedom is truly necessary to recognize the frustration free character of the underlying lattice Hamiltonian. Fundamentally, these degrees of freedom have nothing to do with spectrum of a "guiding-center-only" Hamiltonian. Moreover, such constructions are unfamiliar and not available in the study of simpler (finite range) frustration free lattice Hamiltonians with matrix product ground states (of finite bond dimension). That the zero mode properties of "lattice versions" of pseudopotentials can be understood from a polynomial-free, intrinsically lattice point of view is also suggested by the fact that these pseudopotentials are constructed from an algebra of reasonably simply looking operators. Here we show that zero mode properties, and hence the frustration free character, of these lattice Hamitlonians can be understood as a consequence of algebraic structures that these operators are part of. We believe that our results will deepen insights into parent Hamiltonians of matrix product states with infinite bond dimensions, as could be of use, especially, in the study of fractional Chern insulators.
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