# Fractionally charged excitations on frustrated lattices

## TL;DR

This paper investigates fractional charge excitations in strongly correlated fermion systems on frustrated lattices, revealing confinement, deconfinement points, and the impact on spectral properties through numerical diagonalization.

## Contribution

It provides a detailed numerical study of fractional charges on frustrated lattices, identifying confinement mechanisms and special deconfinement points like the Rokhsar-Kivelson point.

## Key findings

- Ground state degeneracy with long-range order on the checkerboard lattice
- Weak linear confinement of fractional charges leading to large bound states
- Identification of the Rokhsar-Kivelson point with deconfined fractional charges

## Abstract

Systems of strongly correlated fermions on certain geometrically frustrated lattices at particular filling factors support excitations with fractional charges $\pm e/2$. We calculate quantum mechanical ground states, low--lying excitations and spectral functions of finite lattices by means of numerical diagonalization. The ground state of the most thoroughfully studied case, the criss-crossed checkerboard lattice, is degenerate and shows long--range order. Static fractional charges are confined by a weak linear force, most probably leading to bound states of large spatial extent. Consequently, the quasi-particle weight is reduced, which reflects the internal dynamics of the fractionally charged excitations. By using an additional parameter, we fine--tune the system to a special point at which fractional charges are manifestly deconfined--the so--called Rokhsar--Kivelson point. For a deeper understanding of the low--energy physics of these models and for numerical advantages, several conserved quantum numbers are identified.