Quantum thermodynamics of the easy-plane ferromagnetic chain

The thermodynamic properties of the quantum ferromagnetic chain with easy-plane single-ion anisotropy are evaluated over a wide temperature range. The basic theoretical method is a recently proposed one, called the pure-quantum self-consistent harmonic approximation (PQSCHA), which, starting from the original Hamiltonian operator scrĤ, allows the definition of an effective classical Hamiltonian ${\mathit{scrH}}_{\mathrm{eff}}$. We use the Villain transformation to canonical conjugate variables, in order to treat the quantum renormalizations within this framework. In the resulting effective Hamiltonian we restore classical spin variables, according to the classical counterpart of the Villain transformation. Provided that the quantum coupling parameter (which depends on the spin value and on the anisotropy constant) is not too large, this effective Hamiltonian is able to account for the quantum behavior, by means of classical-like calculations. We present a number of results for various quantum thermodynamic quantities, obtained numerically by the classical transfer-matrix method. Moreover, we also calculate static spin correlation functions. Finally, the case of the real ferromagnet ${\mathrm{CsNiF}}_3$ is considered; even though the corresponding easy-plane anisotropy is rather weak, the experimental data for this system are shown to be well reproduced.