Photoemission spectra of the t-J model in 1 and 2D: similarities and differences

TL;DR

This study uses exact diagonalization to analyze the spectral functions of the 1D and 2D t-J models, revealing patterns of spinon and holon excitations and their similarities and differences across dimensions.

Contribution

It provides a detailed comparison of spectral features in 1D and 2D t-J models, highlighting the existence of specific bands and their relation to experimental shadow bands.

Findings

In 1D, spectral features are uniquely assigned to spinon and holon momenta.

In 2D, the t-band exists but is diffuse and does not reach E_F at half filling.

Doped 2D systems show spectral features similar to 1D, including main and shadow bands.

Abstract

We present an exact diagonalization study of the single particle spectral function in the 1D and 2D t-J model. By studying the scaling properties with J and t we find a simple building pattern in 1D and show that every spectral feature can be uniquely assigned by a spinon and holon momentum. We find two types of low energy excitations: a band with energy scale J and high spectral weight disperses upwards in the interior part of the Brillouin zone and reaches E_F at k_F, and a band with energy scale t and low spectral weight disperses downwards in the outer part of the zone, touching E_F at 3k_F. An analogous analysis of the 2D case at half filling shows that the t-band exists also in this case, but is diffuse and never reaches the Fermi energy. For the doped case in 2D the picture is more reminiscent of 1D, in particular the `main-band' with a dispersion proportional J and the `shadow band' with energy scale t can be identified also in this case. This leads us to propose that the shadow bands discovered by Aebi et al. in Bi2212 are the 2D analogue of the 3k_F singularity in 1D systems and unrelated to antiferromagnetic spin fluctuations.