Auxiliary-fermion approach to critical fluctuations in the two-dimensional quantum antiferromagnetic Heisenberg model -: art. no. 174445

The nearest-neighbor quantum antiferromagnetic (AF) Heisenberg model for spin-1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Q(i)=1 on each lattice site i, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, xi(T)proportional toexp(aJ/T), come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T. This drawback, which is caused by overdamping, is overcome in a minimal self-consistent approximation (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths lambda>xi and in the short-range-order regime at lambda