Quantum Hall effect and the relative index for projections.
Quantum Hall effect and the relative index for projections.
复制标题
量子霍尔效应和投影的相对指数。
DOI：
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发表时间：
1990
影响因子：
8.6
通讯作者：
B. Simon
中科院分区：
文献类型：
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作者：
J. Avron;R. Seiler;B. Simon
我们定义Hilbert空间上一对无限维投影的相对指标Index(P，Q)为整数，它是DIM(P)-DIM(Q)在有限维向量空间中的自然推广。结果表明，平面内独立电子的霍尔电导是量子通量不同的哈密顿量的P和Q投射到费米能量以下的态的相对指数，并且费米能量被适当地放置。这种方法与贝利萨德将霍尔电导作为指数的解释密切相关，并揭示了这一点。
We define the relative index, Index(P,Q), for a pair of infinite-dimensional projections on a Hilbert space to be the integer that is the natural generalization of dim(P)-dim(Q) in finite-dimensional vector spaces. We show that the Hall conductance for independent electrons in the plane is the relative index where P and Q project on the states below the Fermi energy for Hamiltonians that differ by a quantum flux and the Fermi energy is appropriately placed. This approach is closely related to, and sheds light on, Bellissard’s interpretation of the Hall conductance as an index.