arXiv 1409.45312014-09cond-mat.dis-nncond-mat.str-el

安德森局域化的临界温度分布

Distribution of critical temperature at Anderson localization

Rayda Gammag, Ki-Seok Kim

发表信息：: Phys. Rev. B 93, 205128 (2016)
DOI：: 10.1103/PhysRevB.93.205128

摘要：

在安德森局域化的基础上，利用局域平均场论，我们从无序度的分布函数中得到了临界温度的分布函数。这种局部平均场论方法的一个要点是引入了波函数多重分形的信息。近藤温度的分布函数（$T_{K}$）在$T_{K} \rightarrow 0$的极限下显示出幂律尾部，而与近藤耦合常数无关。我们还发现，铁磁转变温度（$T_{c}$）的分布函数给出了一个幂律行为的限制时，$T_{c} \rightarrow 0$的铁磁不稳定性的相互作用参数低于一个临界值。然而，$T_{c}$分布函数在$T_{c} \rightarrow 0$极限下停止幂律增加行为，并且在铁磁相内的临界相互作用参数之外消失。这些结果意味着，典型的近藤温度的几何平均值总是消失，由于在$T_{K} \rightarrow 0$极限的分布函数的有限密度，而典型的铁磁转变温度显示出相变在临界相互作用参数。我们建议，典型的转变温度为量子格里菲斯现象与模糊过渡的标准：量子格里菲斯现象发生在临界温度以上的典型值，而模糊相变的结果在低温下的典型转变温度。我们推测，在低温下，安德森局域化的铁磁相变表现出从量子Griffiths现象到临界相互作用参数附近的模糊相变的演化过程。

英文摘要：

Based on a local mean-field theory approach at Anderson localization, we find a distribution function of critical temperature from that of disorder. An essential point of this local mean-field theory approach is that the information of the wave-function multifractality is introduced. The distribution function of the Kondo temperature ($T_{K}$) shows a power-law tail in the limit of $T_{K} \rightarrow 0$ regardless of the Kondo coupling constant. We also find that the distribution function of the ferromagnetic transition temperature ($T_{c}$) gives a power-law behavior in the limit of $T_{c} \rightarrow 0$ when an interaction parameter for ferromagnetic instability lies below a critical value. However, the $T_{c}$ distribution function stops the power-law increasing behavior in the $T_{c} \rightarrow 0$ limit and vanishes beyond the critical interaction parameter inside the ferromagnetic phase. These results imply that the typical Kondo temperature given by a geometric average always vanishes due to finite density of the distribution function in the $T_{K} \rightarrow 0$ limit while the typical ferromagnetic transition temperature shows a phase transition at the critical interaction parameter. We propose that the typical transition temperature serves a criterion for quantum Griffiths phenomena vs. smeared transitions: Quantum Griffiths phenomena occur above the typical value of the critical temperature while smeared phase transitions result at low temperatures below the typical transition temperature. We speculate that the ferromagnetic transition at Anderson localization shows the evolution from quantum Griffiths phenomena to smeared transitions around the critical interaction parameter at low temperatures.

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