# Strongly repulsive anyons in one dimension

## TL;DR

This paper develops perturbative analytic expressions for the static properties of one-dimensional anyon-Hubbard models in the Mott insulating phase, facilitating experimental analysis without extensive numerical simulations.

## Contribution

It provides the first high-order perturbation theory results for anyonic systems, valid for any fractional phase, and benchmarks them against exact numerical methods.

## Key findings

- Analytic expressions for ground-state energy, excitation energies, and momentum distribution up to 6th order.
- Results are valid for any fractional phase of anyons, aiding experimental analysis.
- Benchmarking shows good agreement with density-matrix renormalization group calculations.

## Abstract

To explore the static properties of the one-dimensional anyon-Hubbard model for a mean density of one particle per site, we apply perturbation theory with respect to the ratio between kinetic energy and interaction energy in the Mott insulating phase. The strong-coupling results for the ground-state energy, the single-particle excitation energies, and the momentum distribution functions up to 6th order in hopping are benchmarked against the numerically exact (infinite) density-matrix renormalization group technique. Since these analytic expressions are valid for any fractional phase $\theta$ of anyons, they will be of great value for a sufficiently reliable analysis of future experiments, avoiding extensive and costly numerical simulations.