Spectral weight of doping-induced states in the 2D Hubbard model

TL;DR

This study investigates how the spectral weight of doping-induced states in the 2D Hubbard model varies with cutoff energy, revealing implications for interpreting X-ray absorption spectroscopy data.

Contribution

It demonstrates the dependence of spectral weight on cutoff energy choice and clarifies the interpretation of experimental data in the pseudogap regime.

Findings

Spectral weight satisfies $W_+( ext{delta}) \\ge ext{delta}$ below the upper Hubbard band.

Spectral weight remains small and saturates near 0.2-0.3 in the pseudogap energy range.

Analysis of X-ray absorption data depends critically on the integration window definition.

Abstract

The spectral weight of states induced in the Mott gap via hole doping in the two-dimensional Hubbard model is studied within cluster dynamical mean field theory combined with finite-temperature exact diagonalization. If the cutoff energy is chosen to lie just below the upper Hubbard band, the integrated weight per spin is shown to satisfy $W_+(\delta)\ge\delta$ ($\delta$ denotes the total number of holes), in agreement with model predictions by Eskes {\it et al.} [Phys. Rev. Lett. {\bf 67}, 1035 (1991)]. However, if the cutoff energy is chosen to lie in the range of the pseudogap, $W_+(\delta)$ remains much smaller than $\delta$ and approximately saturates near $\delta\approx 0.2...0.3$. The analysis of recent X-ray absorption spectroscopy data therefore depends crucially on the appropriate definition of the integration window.