# One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction

## TL;DR

This paper analyzes the singularities in the spectral functions of a one-dimensional spin-1/2 fermion gas with repulsive interactions, extending beyond low-energy theories and applicable to cold atom experiments.

## Contribution

It provides detailed calculations of spectral function singularities considering energy scales beyond the low-energy limit using pseudofermion dynamical theory.

## Key findings

- Identifies momentum and interaction dependencies of spectral singularities.
- Extends analysis to finite magnetic fields.
- Connects theoretical results to cold atom experimental observations.

## Abstract

The momentum, fermionic density, spin density, and interaction dependencies of the exponents that control the (momentum-energy)-plane singular features of the one-fermion spectral functions of a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction both at zero and finite magnetic field are studied in detail. Our results refer to energy scales beyond the reach of the low-energy Tomonaga-Luttinger liquid and rely on the pseudofermion dynamical theory for integrable models. The one-fermion spectral weight distributions associated with the spectral functions studied in this paper may be observed in systems of spin-1/2 ultra-cold fermionic atoms in optical lattices.