J. Phys. I France
Volume 5, Numéro 8, August 1995
Page(s) 1037 - 1063
DOI: 10.1051/jp1:1995182
J. Phys. I France 5 (1995) 1037-1063

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

C. Zhou and H.J. Schulz

Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France

(Received 24 January 1995, accepted 2 May 1995)

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.

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