Spin-wave thermodynamics of square-lattice antiferromagnets revisited

Modifying the conventional spin-wave theory in a novel manner based on the Wick decomposition, we present an elaborate thermodynamics of square-lattice quantum antiferromagnets. Our scheme is no longer accompanied by the notorious problem of an artificial transition to the paramagnetic state inherent in modified spin waves in the Hartree-Fock approximation. In the cases of spin $\frac{1}{2}$ and spin $1$, various modified-spin-wave findings for the internal energy, specific heat, static uniform susceptibility, and dynamic structure factor are not only numerically compared with quantum Monte Carlo calculations and Lanczos exact diagonalizations but also analytically expanded into low-temperature series. Modified spin waves interacting via the Wick decomposition provide reliable thermodynamics over the whole temperature range of absolute zero to infinity. Adding higher-order spin couplings such as ring exchange interaction to the naivest Heisenberg Hamiltonian, we precisely reproduce inelastic-neutron-scattering measurements of the high-temperature-superconductor-parent antiferromagnet $\mathrm{La}_2\mathrm{CuO}_4$. Modifying Dyson-Maleev bosons combined with auxiliary pseudofermions also yields thermodynamics of square-lattice antiferromagnets free from thermal breakdown, but it is less precise unless temperature is sufficiently low. Applying all the schemes to layered antiferromagnets as well, we discuss the advantages and disadvantages of modified spin-wave and combined boson-pseudofermion representations.