论文标题
重新审视的复合费用理论：无兰道水平投影的微观推导
The composite fermion theory revisited: a microscopic derivation without Landau level projection
论文作者
论文摘要
复合费用（CF）理论既给出了许多分数量子霍尔（FQH）状态的现象学描述，也提供了用于这些拓扑阶段的大规模数值计算的显微镜结构。但是，尚未正式建立将电子的FQH状态映射到整数量子厅（IQH）状态的基本假设。在某种意义上说，微观计算所需的Landau级别（LL）投影是不受控制的和不可预测的。我们严格地得出了电子与CF之间的统一关系，显示后者自然而然地从单个LL内的特殊相互作用出现，而无需手动诉诸任何投影。在此框架中，所有FQH状态从拓扑上等同于常规CF理论（例如Jain Series）所描述的均具有明确得出的精确模型汉密尔顿人，并且我们可以轻松地从相互作用的CF中推广到FQH状态。我们的派生揭示了CF理论与伪电势/杰克多项式结构之间的基本联系，并认为所有Abelian CF状态在物理上都与IQH状态相等，而大量非亚洲CF状态可以系统地构建和分类。我们还讨论了基于CFS作为基本粒子的描述的实验和有效现场理论描述的影响。
The composite fermion (CF) theory gives both a phenomenological description for many fractional quantum Hall (FQH) states, as well as a microscopic construction for large scale numerical calculation of these topological phases. The fundamental postulate of mapping FQH states of electrons to integer quantum Hall (IQH) states of CFs, however, was not formally established. The Landau level (LL) projection needed for the microscopic calculations is in some sense uncontrolled and unpredictable. We rigorously derive the unitary relationship between electrons and the CFs, showing the latter naturally emerge from special interactions within a single LL, without resorting to any projection by hand. In this framework, all FQH states topologically equivalent to those described by the conventional CF theory (e.g. the Jain series) have exact model Hamiltonians that can be explicitly derived, and we can easily generalise to FQH states from interacting CFs. Our derivations reveal fundamental connections between the CF theory and the pseudopotential/Jack polynomial constructions, and argue that all Abelian CF states are physically equivalent to the IQH states, while a plethora of non-Abelian CF states can be systematically constructed and classified. We also discuss about implications to experiments and effective field theory descriptions based on the descriptions with CFs as elementary particles.
