Charge dynamics in half-filled Hubbard chains with finite on-site interaction

TL;DR

This paper investigates the charge dynamics of the half-filled one-dimensional Hubbard model with finite on-site interaction U, revealing how spectral features evolve with U and identifying key singularities and transitions.

Contribution

It provides a detailed analysis of the charge dynamic structure factor using numerical and analytical methods, highlighting the spectral weight transfer and singularities across the Mott transition.

Findings

Spectral weight shifts from two-holon to electron-hole continuum as U varies.

Power-law singularities are described by SU(2)-invariant impurity models.

A Van Hove singularity causes a sharp spectral feature near the zone boundary.

Abstract

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U\to \infty and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U\to 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and \eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U=0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a Van Hove singularity that persists as a consequence of integrability.