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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Quantum percolation on Lieb Lattices.

W S Oliveira¹, J Pimentel de Lima², Raimundo R Dos Santos¹

¹Universidade Federal do Rio de Janeiro, Instituto de Física, Caixa Postal 68.528, 21941-972 Rio de Janeiro, Rio de Janeiro, Brazil.

Physical Review. E

|April 18, 2025

Summary

This summary is machine-generated.

We investigated quantum percolation on Lieb lattices, finding a localized-delocalized transition. This transition and critical exponents suggest quantum percolation on Lieb lattices belongs to the same universality class across dimensions.

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Area of Science:

Condensed Matter Physics
Statistical Mechanics
Quantum Mechanics

Background:

Percolation theory studies the connectivity of random networks.
Quantum percolation extends these concepts to quantum systems, exploring localization-delocalization transitions.
Lieb lattices offer unique geometric properties for studying such phenomena.

Purpose of the Study:

To theoretically investigate quantum site- and bond-percolation on two- and three-dimensional Lieb lattices.
To determine percolation thresholds and critical exponents using advanced theoretical methods.
To classify the universality class of quantum percolation on these lattices.

Main Methods:

Theoretical investigation employing random matrix theory to analyze energy level statistics.
Numerical simulations utilizing finite-size scaling theory for accurate threshold and exponent estimation.
Analysis of level spacing distributions to identify critical behavior.

Main Results:

Accurate estimates for site- and bond-percolation thresholds and critical exponents were obtained.
A localized-delocalized transition was confirmed at a finite threshold, decreasing with increased coordination number.
Quantum site- and bond-percolation on Lieb lattices were shown to belong to the same universality class.

Conclusions:

The localization length exponent decreases with lattice dimensionality, mirroring classical percolation.
In three dimensions, quantum percolation on Lieb lattices shares universality with the Anderson impurity model.
These findings provide crucial insights into the fundamental nature of quantum phase transitions in disordered systems.