Low-energy local density of states of the 1D Hubbard model

TL;DR

This paper investigates the low-energy local density of states in the 1D Hubbard model, revealing complex spin-charge excitations and boundary effects that influence tunneling in quantum wires, with implications for scanning tunneling spectroscopy.

Contribution

It provides a combined numerical and analytical analysis of the local DOS in the 1D Hubbard model, highlighting deviations from standard Luttinger liquid theory in finite systems.

Findings

Eigenstates show separated spin and charge excitations.

Local DOS exhibits rich spatial and energy structure.

Boundary exponents can be negative, increasing DOS near edges.

Abstract

We examine the local density of states (DOS) at low energies numerically and analytically for the Hubbard model in one dimension. The eigenstates represent separate spin and charge excitations with a remarkably rich structure of the local DOS in space and energy. The results predict signatures of strongly correlated excitations in the tunneling probability along finite quantum wires, such as carbon nanotubes, atomic chains or semiconductor wires in scanning tunneling spectroscopy (STS) experiments. However, the detailed signatures can only be partly explained by standard Luttinger liquid theory. In particular, we find that the effective boundary exponent can be negative in finite wires, which leads to an increase of the local DOS near the edges in contrast to the established behavior in the thermodynamic limit.