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

Abstract

The t-J model for the doped two-dimensional Heisenberg quantum antiferromagnet is studiedin the generalized Dyson-Maleev representation, applying a new continuous unitary transformation which eliminates the coupling of spinand 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 couplingholes and spin-waves is performed simultaneously. The associated one-particle ground state is lower in energy than the corresponding perturbative result, which isreproduced upon application of subsequent transformations.