Optical conductivity of the half-filled Hubbard chain

TL;DR

This paper combines analytical and numerical techniques to comprehensively analyze the optical conductivity of a one-dimensional Mott-Hubbard insulator at zero temperature, revealing detailed spectral features across different interaction strengths.

Contribution

It provides the first complete spectrum of optical conductivity for the model using both DMRG and exact field-theoretical methods, covering all but very small couplings.

Findings

Conductivity shows a square-root increase above the Lieb-Wu gap.

A sharp maximum appears just above the gap for small to moderate interactions.

A secondary weak feature emerges at larger interactions.

Abstract

We combine well-controlled analytical and numerical methods to determine the optical conductivity of the one-dimensional Mott-Hubbard insulator at zero temperature. A dynamical density-matrix renormalization group method provides the entire absorption spectrum for all but very small coupling strengths. In this limit we calculate the conductivity analytically using exact field-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a characteristic square-root increase. For small to moderate interactions, a sharp maximum occurs just above the gap. For larger interactions, another weak feature becomes visible around the middle of the absorption band.