CRITICAL AND BICRITICAL PROPERTIES OF HARPERS EQUATION WITH NEXT-NEAREST-NEIGHBOR COUPLING
CRITICAL AND BICRITICAL PROPERTIES OF HARPERS EQUATION WITH NEXT-NEAREST-NEIGHBOR COUPLING
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DOI：
10.1103/physrevb.50.11365
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发表时间：
1994-10-15
影响因子：
3.7
通讯作者：
KOHMOTO, M
中科院分区：
文献类型：
--
作者：
HAN, JH;THOULESS, DJ;KOHMOTO, M
我们已经利用了各种技术来研究哈珀方程的标度性质的普遍性和稳定性，当耦合到下一个最近的网站时，在规范场的存在下，紧束缚正方形晶格上运动的粒子的方程。我们发现，从数值和分析研究，标度行为的频谱的总宽度和多重分形性质的频谱是不变的，提供的次近邻耦合项低于一定的阈值。临界性不需要哈密顿量的完全平方对称性，但平方对角线应保持为反射线。在最近邻项占主导地位的区域和次最近邻项占主导地位的区域之间的边界处发现双临界线。在双临界线上发现了不同的谱宽临界指数和不同的多重分形行为，在次近邻项占主导地位的区域，如果哈密顿量在平行于正方形边的方向上反射不变，则多重分形行为仍然是临界的，但新的长度尺度进入，多重分形行为不再是普适的，而是表现出强烈的振荡行为。对于每单位晶胞的通量等于1/q，光谱的测量在这个区域中与1/q成比例，但是如果它是斐波那契数的比率，则测量随着分母的相反幂而减小。
We have exploited a variety of techniques to study the universality and stability of the scaling properties of Harper’s equation, the equation for a particle moving on a tight-binding square lattice in the presence of a gauge field, when coupling to next-nearest sites is added. We find, from numerical and analytical studies, that the scaling behavior of the total width of the spectrum and the multifractal nature of the spectrum are unchanged, provided the next-nearest-neighbor coupling terms are below a certain threshold value. The full square symmetry of the Hamiltonian is not required for criticality, but the square diagonals should remain as reflection lines. A bicritical line is found at the boundary between the region in which the nearest-neighbor terms dominate and the region in which the next-nearest-neighbor terms dominate. On the bicritical line a different critical exponent for the width of the spectrum and different multifractal behavior are found. In the region in which the next-nearest-neighbor terms dominate, the behavior is still critical if the Hamiltonian is invariant under reflection in the directions parallel to the sides of the square, but a new length scale enters, and the behavior is no longer universal but shows strongly oscillatory behavior. For a flux per unit cell equal to 1/q the measure of the spectrum is proportional to 1/q in this region, but if it is a ratio of Fibonacci numbers the measure decreases with a rather higher inverse power of the denominator.