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The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an importantmodel system for the high-$T_c$ superconductors based on cuprates. Using thetechnique of self-similar continuous unitary transformations we deriveeffective Hamiltonians for the charge motion in these ladders. The keyadvantage of this technique is that it provides effective models explicitly inthe thermodynamic limit. A real space restriction of the generator of thetransformation allows us to explore the experimentally relevant parameterspace. From the effective Hamiltonians we calculate the dispersions for singleholes. Further calculations will enable the calculation of the interaction oftwo holes so that a handle of Cooper pair formation is within reach.

Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations