Quantum $k$-core conduction on the Bethe lattice

Details Quantum $k$-core conduction on the Bethe lattice Quantum $k$-core conduction on the Bethe lattice

2010-05-25

arxiv.org/abs/1005.4673v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pgs., 6 figs

Scientific paper

Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least $k-1$ neighboring occupied bonds, i.e. $k$-core diluted. In the classical case, we find the onset of conduction for $k=2$ is continuous, while for $k=3$, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupied bond as a random scatterer, we find for $k=3$ that the random first-order phase transition in the geometry also drives the onset of quantum conduction giving rise to a new universality class of Anderson localization transitions.

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