Quantum percolation on Lieb Lattices

TL;DR

This paper investigates quantum percolation on Lieb lattices across dimensions, analyzing energy level statistics to identify phase transitions and universality classes, with implications for understanding localization phenomena.

Contribution

It provides the first detailed analysis of quantum percolation on Lieb lattices, determining critical thresholds, exponents, and universality classes in 2D and 3D.

Findings

Supports a finite threshold localized-delocalized transition

Localization length exponent decreases with lattice dimension

Quantum percolation on Lieb lattices shares universality class with Anderson model

Abstract

We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with $\nu$ decreasing with lattice dimensionality, $d$, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.