On a Network Model of Localization in a Random Magnetic Field

Дата и время публикации : 1995-06-21T18:35:17Z

Авторы публикации и институты :
Yong Baek Kim
Akira Furusaki
Derek K. K. Lee

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: Revtex, 6 pages, 3 figures appended as an uuencoded file
Первичная категория: cond-mat

Все категории : cond-mat

Краткий обзор статьи: We consider a network model of snake states to study the localization problem of non-interacting fermions in a random magnetic field with zero average. After averaging over the randomness, the network of snake states is mapped onto $M$ coupled SU$(2N)$ spin chains in the $N rightarrow 0$ limit. The number of snake states near the zero-field contour, $M$, is an even integer. In the large conductance limit $g = M {e^2 over 2 pi hbar}$ ($M gg 2$), it turns out that this system is equivalent to a particular representation of the ${rm U}(2N) / {rm U}(N) times {rm U}(N)$ sigma model ($N rightarrow 0$) {it without} a topological term. The beta function $beta (1/M)$ of this sigma model in the $1/M$ expansion is consistent with the previously known $beta (g)$ of the unitary ensemble. These results and further plausible arguments support the conclusion that all the states are localized.

Category: Physics