Drude Weight of the Two-Dimensional Hubbard Model -- Reexamination of Finite-Size Effect in Exact Diagonalization Study --

TL;DR

This study reexamines the finite-size effects on the Drude weight in the 2D Hubbard model using exact diagonalization, revealing insights into the insulator-metal transition and optical conductivity behavior.

Contribution

It introduces improved cluster shapes and boundary conditions in exact diagonalization, providing a more accurate analysis of finite-size effects on the Drude weight.

Findings

Drude weight scales with squared hole doping

Identifies transition from Mott insulator to metal

Mid-gap incoherent part appears faster than coherent part

Abstract

The Drude weight of the Hubbard model on the two-dimensional square lattice is studied by the exact diagonalizations applied to clusters up to 20 sites. We carefully examine finite-size effects by consideration of the appropriate shapes of clusters and the appropriate boundary condition beyond the imitation of employing only the simple periodic boundary condition. We successfully capture the behavior of the Drude weight that is proportional to the squared hole doping concentration. Our present result gives a consistent understanding of the transition between the Mott insulator and doped metals. We also find, in the frequency dependence of the optical conductivity, that the mid-gap incoherent part emerges more quickly than the coherent part and rather insensitive to the doping concentration in accordance with the scaling of the Drude weight.