One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields

TL;DR

This paper analyzes the spectral functions of the 1D Fermionic Hubbard model with one fermion per site, exploring the effects of magnetic fields and interactions on the Mott-Hubbard insulator's properties.

Contribution

It provides a non-perturbative calculation of the spectral functions and Mott-Hubbard gap at various spin densities and magnetic fields, advancing understanding of correlated 1D systems.

Findings

Calculated the Mott-Hubbard gap for all spin densities and interactions.

Described the spectral function line shapes near cusp singularities.

Discussed differences between Mott-Hubbard and doped insulators.

Abstract

Here the line shape of the up- and down-spin one-particle spectral functions at and in the (k,energy)-plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved non-perturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/2 atom systems is discussed.