Critical Properties in Dynamical Charge Correlation Function for the One-Dimensional Mott Insulator

TL;DR

This paper investigates the critical behavior of the dynamical charge correlation function in a one-dimensional Mott insulator, revealing the role of spinon excitations and calculating critical exponents using Bethe ansatz.

Contribution

It demonstrates the importance of final-state interactions in charge correlations and derives momentum-dependent critical exponents for the model.

Findings

Edge singularity governed by massless spinons

Critical exponents depend on momentum

Final-state interactions are crucial in charge dynamics

Abstract

Critical properties in the dynamical charge correlation function for the one-dimensional Mott insulator are studied. By properly taking into account {\it the final-state interaction} between the charge and spin degrees of freedom, we find that the edge singularity in the charge correlation function is governed by massless spinon excitations, although it is naively expected that spinons do not directly contribute to the charge excitation over the Hubbard gap. We obtain the momentum-dependent anomalous critical exponent by applying the finite-size scaling analysis to the Bethe ansatz solution of the half-filled Hubbard model.