# Partial Fermionization---Spectral Universality in 1D Repulsive Bose Gases

## TL;DR

This paper uncovers universal spectral features in one-dimensional repulsive Bose gases, showing a smooth transition from ideal Bose behavior to fermionization, with analytical results matching experimental and numerical data.

## Contribution

It introduces a nonperturbative analytical approach combining quantum cluster expansions and dynamical information to describe partial fermionization in 1D Bose gases.

## Key findings

- Universal spectral crossover observed in 1D Bose gases.
- Analytical results agree with numerical simulations and experiments.
- Method predicts excitation spectra for thermodynamics analysis.

## Abstract

Due to the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with repulsive short-range interactions. We show that the crossover from an ideal Bose gas to the strongly correlated, fermionized gas, i.e., partial fermionization, exhibits universal behavior: Systems with very few up to many particles share the same underlying spectral features. In our derivation we supplement quantum cluster expansions with short-time dynamical information. Our nonperturbative analytical results are in excellent agreement with numerics for systems of experimental relevance in cold atom physics, such as interacting bosons on a ring (Lieb-Liniger model) or subject to harmonic confinement. Our method provides predictions for excitation spectra that enable access to finite-temperature thermodynamics in large parameter ranges.