Magnetic excitation spectra of strongly correlated quasi-one dimensional systems: Heisenberg versus Hubbard-like behavior

TL;DR

This study compares the spin excitation spectra of Hubbard and Heisenberg models in quasi-one-dimensional systems, revealing that Hubbard spectra resemble Heisenberg spectra at intermediate interaction strengths, with implications for experimental analysis.

Contribution

It provides a detailed comparison of Hubbard and Heisenberg models' spin spectra in quasi-one-dimensional systems, highlighting the conditions under which they are similar.

Findings

Hubbard spectra resemble Heisenberg spectra at U/t ~ 2-3

Low-energy peaks indicate spinonic excitations in both models

Ratios of peak intensities evolve slowly with increasing U/t

Abstract

We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum -- with low-energy peaks resembling spinonic excitations -- already at intermediate on-site repulsion as small as $U/t \sim 2-3$, although ratios of peak intensities at different momenta continue evolving with increasing $U/t$ converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of $U/t$ of quasi-one dimensional systems described by one-orbital Hubbard models from experimental information.