Bethe strings in the spin dynamical structure factor of the Mott-Hubbard phase in one-dimensional fermionic Hubbard model

TL;DR

This paper investigates how Bethe strings influence the spin dynamical structure factor in the one-dimensional fermionic Hubbard model, revealing their role in spectral features and the effects of electron itinerancy on spin dynamics.

Contribution

It provides a detailed analysis of Bethe strings' impact on the spin dynamical structure factor in the Hubbard model, especially near the lower thresholds, extending understanding beyond the Heisenberg limit.

Findings

Bethe strings contribute to a gapped continuum in the spin structure factor.

The contribution of Bethe strings to zz correlations diminishes with increasing spin density.

Electron itinerancy significantly affects the spectral line shape and spin dynamics.

Abstract

The spectra and role in the spin dynamical properties of bound states of elementary magnetic excitations named Bethe strings that occur in some integrable spin and electronic one-dimensional models have recently been identified and realized in several materials by experiments. Corresponding theoretical studies have usually relied on the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field. At the isotropic point, it describes the large onsite repulsion U limit of the spin degrees of freedom of the one-dimensional fermionic Hubbard model with one electron per site in a magnetic field h. In this paper we consider the thermodynamic limit and study the effects of lowering the latter quantum problem ratio u=U/4t, where t is the first-neighbor transfer integral, on the line-shape singularities in regions at and just above the lower thresholds of the transverse and longitudinal spin dynamical structure factors. The most significant spectral weight contribution from Bethe strings leads to a gapped continuum in the spectrum of the spin dynamical structure factor +-. Our study focuses on the line shape singularities at and just above the gapped lower threshold of that continuum, which have been identified in experiments. Our results are consistent with the contribution of Bethe strings to the spin dynamical structure factor zz being small at low spin densities and becoming negligible upon increasing that density. Our results provide physically important information about how electron itinerancy affects the spin dynamics.