Dynamics of a Hole in the Large-U Hubbard Model: A Feynman Diagram Approach

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 developed 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