Effects of Next-Nearest-Neighbor Hopping on the Hole Motion in an Antiferromagnetic Background

TL;DR

This study investigates how next-nearest-neighbor hopping influences hole dynamics in antiferromagnetic materials, providing exact solutions in large dimensions and exploring spectral functions in two dimensions.

Contribution

It offers an exact Green function analysis in large dimensions and extends the understanding of hole spectra to finite dimensions with next-nearest-neighbor hopping.

Findings

Exact density of states in large dimensions calculated.

Discrete spectra become continuum with added resonances in 2D.

Spectral features are governed by parameters t and J.

Abstract

In this paper we study the effect of next-nearest-neighbor hopping on the dynamics of a single hole in an antiferromagnetic (N\'{e}el) background. In the framework of large dimensions the Green function of a hole can be obtained exactly. The exact density of states of a hole is thus calculated in large dimensions and on a Bethe lattice with large coordination number. We suggest a physically motivated generalization to finite dimensions (e.g., 2 and 3). In $d=2$ we present also the momentum dependent spectral function. With varying degree, depending on the underlying lattice involved, the discrete spectrum for holes is replaced by a continuum background and a few resonances at the low energy end. The latter are the remanents of the bound states of the $t-J$ model. Their behavior is still largely governed by the parameters $t$ and $J$. The continuum excitations are more sensitive to the energy scales $t$ and $t_1$.