The two-dimensional quantum Heisenberg antiferromagnet: effective Hamiltonian approach to the thermodynamics

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Abstract
We study the thermodynamic properties of the 2d quantum Heisenberg antiferromagnet on the square lattice, by means of the pure-quantum self-consistent harmonic approximation, that reduces the quantum spin system to an effective classical one, with an effective exchange integral. Several physical observables are obtained in a simple way from their classical counterparts, evaluated by classical Monte Carlo simulations with the effective Hailtonian. Internal energy, specific heat, correlation functions, staggered susceptibility, and correlation length are shown for different spin values, and compared with the available high-temperature expansion and quantum Monte Carlo results, as well as with experimental data. We also discuss other theoretical approaches, especially the link with the quantum nonlinear sigma model.

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