Dynamics of a hole in the large--U Hubbard model: a Feynman diagram approach

TL;DR

This paper develops a diagrammatic approach to study the dynamics of a single hole in the large-U Hubbard model, revealing the role of vertex corrections and connecting weak and strong coupling theories.

Contribution

It introduces a nonlocal Bogolyubov transformation and a systematic diagrammatic scheme to analyze hole dynamics, including the Trugman process, in the Hubbard model.

Findings

Good agreement with previous theories and small-cluster calculations

Dominance of vertex corrections in the Trugman process

Link between weak and strong coupling regimes

Abstract

We study the dynamics of a single hole in an otherwise half--filled two--dimensional Hubbard model by introducing a nonlocal Bogolyubov transformation in the antiferromagnetic state. This allows us to rewrite the Hamiltonian in a form that makes a separation between high--energy processes (involving double--occupancy) and low--energy physics possible. A diagrammatic scheme is developped that allows for a systematic study of the different processes delocalizing a carrier in the antiferromagnetic state. In particular, the so--called Trugman process, important if transverse spin fluctuations are neglected, is studied and is shown to be dominated by the leading vertex corrections. We analyze the dynamics of a single hole both in the Ising limit and with spin fluctuations. The results are compared with previous theories as well as with recent exact small--cluster calculations, and we find good agreement. The formalism establishes a link between weak and strong coupling methodologies.