Eur. Phys. J. B 84, 475-490 (2011)
https://doi.org/10.1140/epjb/e2011-20150-x

Regular Article

Hole dispersions for antiferromagnetic spin-$\frac{\mathrm{1}}{\mathrm{2}}$ two-leg ladders by self-similar continuous unitary transformations

Lehrstuhl für Theoretische Physik I, Technische Universität Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany

^a e-mail: goetz.uhrig@tu-dortmund.de

Received: 1 March 2011
Received in final form: 25 July 2011
Published online: 23 November 2011

Abstract

The hole-doped antiferromagnetic spin-$\frac{\mathrm{1}}{\mathrm{2}}$ two-leg ladder is an important model system for the high-T_c superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach.