Umklapp scattering in the one-dimensional Hubbard model

TL;DR

This paper investigates the specific role of Umklapp scattering in driving the Mott metal-insulator transition within the one-dimensional Hubbard model, distinguishing it from normal scattering effects.

Contribution

It introduces a method to separately analyze Umklapp and normal scattering processes, revealing their distinct impacts on the Mott charge gap.

Findings

Umklapp scattering is responsible for the Mott charge gap.

Normal scattering strongly renormalizes the charge gap.

Interplay between scattering types influences charge dynamics.

Abstract

The Mott metal-insulator transition is a typical strong correlation effect triggered by the Umklapp scattering. However, in a physical system, the Umklapp scattering coexists with the normal scattering, including both forward and backward scattering, which conserves the total momentum of scattered electrons. Therefore, it is not easy to quantify the contribution of the Umklapp scattering in a Mott metal-insulator transition. To resolve this difficulty, we propose to explore these scattering processes separately. We study the contribution of each scattering process in the one-dimensional Hubbard model using the momentum-space density-matrix renormalization group (kDMRG) and bosonization methods. Our kDMRG calculation confirms that the Mott charge gap results from the Umklapp scattering, but the normal scattering processes strongly renormalize its value. Furthermore, we present a scaling analysis of the Mott charge gap in the bosonization theory and show that the interplay between the Umklapp and forward scattering dictates the charge dynamics in the half-filled Hubbard model.