GENERALIZED DYSON-MALEEV REPRESENTATION OF DOPED AND UNDOPED HEISENBERG ANTIFERROMAGNETS

The doped and undoped Heisenberg antiferromagnet is described within a rigorous and unified theoretical framework based on ideas of Dyson. T he unified description is achieved by means of a particular representa tion of the relevant operators, referred to as generalized Dyson-Malee v (DM) representation, where the kinematic constraints are fully taken into account by means of a projection operator. The latter, whose exp licit analytic form is derived, commutes with the Hamiltonian, and its main effect is that the representation vanishes on the whole unphysic al subspace. On the physical subspace, our representation is similar t o that proposed by Schmitt-Rink et al., and coincides with the latter in the linear spin-wave approximation. In the absence of holes, the ge neralized DM representation properly reduces to the ordinary DM repres entation of spin-1/2 operators. One of the main results of our approac h is that the projection operator has no effect on the eigenvalues, bu t does affect the eigenstates and, hence, expectation values and corre lation functions. As in the original Dyson theory, there is thus a cle ar separation of kinematic and dynamic effects. Finally, the case of a single hole is treated in some detail. Guided by the formal similarit y with the Frohlich polaron model, the Hamiltonian is subject to a uni tary transformation, which is the lattice version of the Jest transfor mation, well-known in polaron theory. The result of the transformation is that the Hamiltonian assumes diagonal form in the hole operators.