Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

TL;DR

This paper investigates fractional boundary charges in strongly interacting one- and two-dimensional systems, revealing quantized slopes and degeneracies that serve as probes for interacting phases.

Contribution

It introduces a unified analysis of fractional boundary charges in strongly interacting systems, linking boundary charge behavior to topological degeneracies and quantized slopes.

Findings

FBC depends linearly on phase offset with quantized slope in nanowires.

FBC depends linearly on flux with quantized slope in fractional quantum Hall systems.

Different FBC values at fixed parameters indicate degenerate ground states.

Abstract

We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors $\nu=1/(2l+1)$, where $l$ is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has $2l+1$ different branches that cannot be connected adiabatically, reflecting the $(2l+1)$-fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.