From quantum to classical calculations via an effective Hamiltonian approach: The easy-axis two-dimensional quantum antiferromagnet

We have applied the semiclassical method called pure-quantum self-consistent harmonic approximation (PQSCHA) to the study of thermodynamics of the easy-axis quantum Heisenberg antiferromagnet on the square lattice. By this approach, the complex and time consuming path integral quantum Monte Carlo calculations can be reduced to classical ones by means of an effective hamiltonian approach based on path integral formalism. Furthermore, a novel Trotter extrapolation, based on our approach, can be proposed, strongly reducing the requested Trotter number with a good accuracy. The model we have studied is known to have an Ising-like transition at a classical level, due to the presence of the anisotropy term, and consequently represents a good candidate for describing the main features of the thermodynamics of the real compound Rb2MnF4, showing a phase transition to 2d order, and a 2d behaviour for every experimentally investigated temperature. The PQSCHA provides an accurate description of the model both above and below the phase transition and accounts quantitatively for the quantum effects. A comparison with the experimental data available for Rb2MnF4 shows that the model describes quantitatively the thermodynamics of the compound, giving in particular an accurate estimate of its critical temperature.