Quantum and classical localization and the Manhattan lattice

被引:8
作者
Beamond, EJ
Owczarek, AL
Cardy, J
机构
[1] Univ Oxford, Oxford OX1 3NP, England
[2] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia
[3] Univ Oxford All Souls Coll, Oxford OX1 4AL, England
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2003年 / 36卷 / 41期
关键词
D O I
10.1088/0305-4470/36/41/001
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider a network model, embedded on the Manhattan lattice, of a quantum localization problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are invariant under spin rotations but not under time reversal. A mapping exists between problems belonging to this symmetry class and certain classical random walks which are self-avoiding and have attractive interactions; we exploit this equivalence, using a study of the classical random walks to gain information about the corresponding quantum problem. In a field-theoretic approach, we show that the interactions may flow to one of two possible strong-coupling regimes separated by a transition: however, using Monte Carlo simulations we show that the walks are in fact always compact two-dimensional objects with a well-defined one-dimensional surface, indicating that the corresponding quantum system is localized.
引用
收藏
页码:10251 / 10267
页数:17
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