Total bandwidth for Harper equation: correction to renormalization analysis
Total bandwidth for Harper equation: correction to renormalization analysis
复制标题
哈珀方程的总带宽：重正化分析的修正
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
Yong
中科院分区：
文献类型：
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作者：
Yong
本文研究了哈珀方程有效哈密顿量在总带宽方面的修正。有效哈密顿量描述了当考虑高阶分数的谱时从低阶分数的谱的进一步分裂。分割子带的总带宽由通过有效哈密顿量在其鞍点处的曲率修改的 Thouless 缩放定律给出。本文证明有效哈密顿量的首项是精确可解的。此外，数值上得到了有效哈密顿量曲率的修正，并找到了显式的解析表达式。这给出了第二个求和规则，该规则对于推导通用分数的 Thouless 缩放定律非常重要。
This paper studies the correction to the effective Hamiltonian of the Harper equation in respect of the total bandwidth. The effective Hamiltonian describes the further splitting from the spectrum of a lower-order fraction when the spectrum of a higher-order fraction is considered. The total bandwidth for a split sub-band is given by the Thouless scaling law modified by the curvature of the effective Hamiltonian at its saddle points. In this paper, it is shown that the leading term of the effective Hamiltonian is exactly solvable. Moreover the correction to the curvature of the effective Hamiltonian is obtained numerically, and the explicit analytical expression is also found. This gives the second sum rule, which is of importance in deriving the Thouless scaling law for a generic fraction.