Scan calculation of the density of states: real space cluster perturbation theory applied to inhomogeneous Hubbard model in one dimension

TL;DR

This paper applies real-space cluster perturbation theory to analyze the density of states in an inhomogeneous one-dimensional Hubbard model, revealing local spectral properties and offering a practical spectroscopy method for ultracold atoms.

Contribution

It extends cluster perturbation theory to inhomogeneous systems, enabling local spectral analysis and providing insights into inhomogeneous Hubbard models.

Findings

Local density of states mirrors homogeneous system with same local filling

Spectral evolution reflects occupancy-dependent features

Method offers a practical spectroscopy tool for ultracold atoms

Abstract

We present the spectral analysis of a one-dimensional Hubbard model with a parabolic potential, using a real-space cluster perturbation theory (rCPT) designed to study spatially inhomogeneous electron systems with strong correlation. It is a natural extension of the conventional CPT to inhomogeneous cases by computing local Green's functions while averaging over multiple cluster boundaries. We find that the local density of states of at each site mirrors that of a homogeneous system with the same local filling. This insight offers a perspective on spectral evolution in inhomogeneous systems used to scan the occupancy-dependent features of the homogeneous system, making this setup a practical one-shot spectroscopy tool for ultracold atoms in harmonic traps.