### Abstract

Quantum k-core percolation is the study of quantum transport on k-core percolation clusters where each occupied bond must have at least k occupied neighboring bonds. As the bond occupation probability p is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the length scale for the disorder l
_{d} is much greater than the coherence length l
_{c}, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrated that for k=3 the metal-insulator transition (MIT) is discontinuous, suggesting a new type of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability p and system size on a Bethe-like lattice. The level spacing analysis suggests that for k=0, p
_{q}, the quantum percolation critical probability, is greater than p
_{c}, the geometrical percolation critical probability, and the transition is continuous. In contrast, for k=3, p
_{q}=p
_{c}, and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new random first-order phase transition and therefore a new universality class of disorder-driven quantum MITs.

Original language | English (US) |
---|---|

Article number | 064206 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 86 |

Issue number | 6 |

DOIs | |

State | Published - Aug 24 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

**Level statistics for quantum k-core percolation.** / Cao, L.; Schwarz, Jennifer M.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 86, no. 6, 064206. https://doi.org/10.1103/PhysRevB.86.064206

}

TY - JOUR

T1 - Level statistics for quantum k-core percolation

AU - Cao, L.

AU - Schwarz, Jennifer M

PY - 2012/8/24

Y1 - 2012/8/24

N2 - Quantum k-core percolation is the study of quantum transport on k-core percolation clusters where each occupied bond must have at least k occupied neighboring bonds. As the bond occupation probability p is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the length scale for the disorder l d is much greater than the coherence length l c, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrated that for k=3 the metal-insulator transition (MIT) is discontinuous, suggesting a new type of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability p and system size on a Bethe-like lattice. The level spacing analysis suggests that for k=0, p q, the quantum percolation critical probability, is greater than p c, the geometrical percolation critical probability, and the transition is continuous. In contrast, for k=3, p q=p c, and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new random first-order phase transition and therefore a new universality class of disorder-driven quantum MITs.

AB - Quantum k-core percolation is the study of quantum transport on k-core percolation clusters where each occupied bond must have at least k occupied neighboring bonds. As the bond occupation probability p is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the length scale for the disorder l d is much greater than the coherence length l c, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrated that for k=3 the metal-insulator transition (MIT) is discontinuous, suggesting a new type of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability p and system size on a Bethe-like lattice. The level spacing analysis suggests that for k=0, p q, the quantum percolation critical probability, is greater than p c, the geometrical percolation critical probability, and the transition is continuous. In contrast, for k=3, p q=p c, and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new random first-order phase transition and therefore a new universality class of disorder-driven quantum MITs.

UR - http://www.scopus.com/inward/record.url?scp=84865654255&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865654255&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.86.064206

DO - 10.1103/PhysRevB.86.064206

M3 - Article

AN - SCOPUS:84865654255

VL - 86

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 6

M1 - 064206

ER -