Quantum $k$-core conduction on the Bethe lattice

TL;DR

This paper investigates classical and quantum conduction on a bond-diluted Bethe lattice with a focus on $k$-core constraints, revealing different transition types and a new universality class for quantum localization.

Contribution

It introduces a $k$-core constrained model for conduction on the Bethe lattice and uncovers novel transition behaviors and universality classes in both classical and quantum regimes.

Findings

Classical $k=2$ conduction transition is continuous.

Classical $k=3$ conduction transition is discontinuous.

Quantum $k=3$ conduction transition is driven by a first-order geometric transition.

Abstract

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.