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Quantum and classical localisation and the Manhattan lattice

E. J. Beamond·A. L. Owczarek·John Cardy
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Abstract

We consider a network model, embedded on the Manhattan lattice, of a quantum localisation 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 localised.

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E. J. Beamond, A. L. Owczarek, John Cardy. 2003-08-19. Quantum and classical localisation and the Manhattan lattice. https://arxiv.org/abs/cond-mat/0210359

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