Corner Charge Fluctuations in Higher Dimensions

TL;DR

This paper extends the study of charge fluctuations and corner contributions from two to higher dimensions, deriving universal angle dependencies and benchmarking predictions with simulations, revealing insights into quantum criticality and geometry.

Contribution

It introduces a systematic framework for corner charge fluctuations in higher dimensions, including universal angle functions and their relation to quantum geometry.

Findings

Derived universal angle dependence for trihedral corners in 3D.

Validated predictions with Monte Carlo simulations at quantum critical points.

Identified wedge-corner contributions probing the quantum metric.

Abstract

Measuring charge fluctuations within a subregion provides a powerful probe of quantum many-body systems. In two spatial dimensions, the shape dependence of the dimensionless corner contribution encodes universal data of quantum critical points and reveals observables of quantum geometry in various quantum phases. Here, we systematically extend this framework to higher dimensions. In three dimensions, we derive the universal angle dependence associated with trihedral corners of a generic parallelepiped and benchmark the predictions against Monte Carlo simulations of lattice models at the O(3) quantum critical point. We further identify a wedge-corner contribution that directly probes the quantum metric, supported by numerical results for a lattice Weyl semimetal model. More generally, we obtain angle functions for polyhedral corners of arbitrary parallelotopes in general dimensions and clarify the scaling of the corner contribution across phases of matter. While insulators and conformal critical points exhibit similar behavior across dimensions, metals display a characteristic even-odd dimensional effect.