Universality of Boundary Charge Fluctuations

TL;DR

This paper introduces a universal method using boundary charge fluctuations to characterize phase transitions in various insulators, revealing dimension-dependent scaling laws near the transition point.

Contribution

It establishes boundary charge fluctuation as a universal tool for identifying phase transitions across different insulator types, including topological, Anderson, and Mott insulators.

Findings

Universal scaling of boundary charge fluctuations with energy gap

Inverse gap scaling in 1D systems

Logarithmic scaling in 2D systems

Abstract

We establish the quantum fluctuations $\Delta Q_B^2$ of the charge $Q_B$ accumulated at the boundary of an insulator as an integral tool to characterize phase transitions where a direct gap closes (and reopens), typically occurring for insulators with topological properties. The power of this characterization lies in its capability to treat different kinds of insulators on equal footing; being applicable to transitions between topological and non-topological band, Anderson, and Mott insulators alike. In the vicinity of the phase transition we find a universal scaling $\Delta Q_B^2(E_g)$ as function of the gap size $E_g$ and determine its generic form in various dimensions. For prototypical phase transitions with a massive Dirac-like bulk spectrum we demonstrate a scaling with the inverse gap in one dimension and a logarithmic one in two dimensions.