Flow equations and new weak-coupling solution for the spin-polaron in a quantum antiferromagnet

The t-J model for the doped two-dimensional Heisenberg quantum antiferromagnet is studied in the generalized Dyson-Maleev representation, applying a new continuous unitary transformation which eliminates the coupling of spin and charge degrees of freedom. The analytical solutions of the resulting flow equations are derived in the weak-coupling regime where t/J is small. This continuous transformation yields a new weak-coupling result for the dispersion of the spin-polaron, if the elimination of both the non-diagonal spin-wave contributions and the terms coupling holes and spin-waves is performed simultaneously. The associated one-particle ground state is lower in energy than the corresponding perturbative result, which is reproduced upon application of subsequent transformations.