Universality of Boundary Charge Fluctuations

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.

arXiv commentIncludes supplemental material

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Cited by in corpus (8)

• Effect of disorder on topological charge pumping in the Rice-Mele model
• Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems
• Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints
• Quantitative analysis of interaction effects in generalized Aubry-Andŕe-Harper models
• Universal properties of boundary and interface charges in multichannel one-dimensional continuum models
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus
• Universal properties of boundary and interface charges in continuum models of one-dimensional insulators