EFFECTIVE-HAMILTONIANS FOR HOLES IN ANTIFERROMAGNETS - A NEW APPROACHTO IMPLEMENT FORBIDDEN DOUBLE OCCUPANCY

A coherent state representation for the electrons of ordered antiferro magnets is used to derive effective Hamiltonians for the dynamics of h oles in such systems. By an appropriate choice of these states, the co nstraint of forbidden double occupancy can be implemented rigorously. Using these coherent states, one arrives at a path integral representa tion of the partition function of the systems, from which the effectiv e Hamiltonians can be read off. We apply this method to the t-J model on the square lattice and on the triangular lattice. In the former cas e, we reproduce the well-known fermion-boson Hamiltonian for a hole in a collinear antiferromagnet. We demonstrate that our method also work s for non-collinear antiferromagnets by calculating the spectrum of a, hole in the triangular antiferromagnet in the self-consistent Born ap proximation and by comparing it with numerically exact results.