Application of Dyson's Transformation to Antiferromagnetic Heisenberg Model : Properties of Ground State

Fumihiko Takano, Taeko Ogawa

Ya. G. Sinaǐ

Klaus Bärwinkel, Heinz–Jürgen Schmidt, Jürgen Schnack

Nikolay M. Plakida

Tsuguhiro Tamaribuchi, M. Ishikawa

Ground-state properties of antiferromagnetic quantum XXZ models on triangular and square lattices are investigated within a framework of conventional perturbative spin-wave theory using the Dyson-Maleev transformation. To lowest order in the perturbation expansion, the ground-state energy, where dynamical interactions are taken into account, the sublattice magnetization, spin-spin correlation functions, and susceptibilities are calculated. Higher-order calculations are made for the correlation functions and for the sublattice magnetization. For the triangular Heisenberg antiferromagnet, divergences in the perturbation expansion of the sublattice magnetization, which means the conventional spin-wave theory based on the sublattice order is not applicable to that system, are shown to exist. Explicit asymptotic behaviors of the correlation functions are also given.

J Stein

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.