The Quantum Self-Consistent Harmonic Approximation: A unified framework for quantum spin systems

The Self-Consistent Harmonic Approximation (SCHA) has been utilized to investigate quantum and thermal phase transitions within magnetic models and, more recently, in spintronic applications. The SCHA methodology involves utilizing simple harmonic Hamiltonians, which are augmented with renormalization parameters that incorporate high-order fluctuations typically overlooked by conventional Linear Spin-Wave (LSW) theories. Although this approach exhibits reasonable accuracy for models defined by large spin values, its reliability diminishes when applied to quantum systems with $S=1/2$. The traditional development of SCHA has incorporated semiclassical assumptions that obscure quantum effects. In this study, we introduce a quantum framework for the SCHA that eliminates the need for semiclassical approximations. Our Quantum Self-Consistent Harmonic Approximation (QSCHA) utilizes the spin coherent states formalism within a fully quantum formulation. Consequently, we derive a novel renormalization parameter that accurately integrates quantum corrections. To assess the efficacy of this new approach, we apply the QSCHA to analyze the critical temperature transitions across various well-documented magnetic models. The findings, combined with the simplified operational procedure relative to other conventional interacting spin-wave methodologies, suggest that QSCHA is a promising tool for advancing research in quantum magnetism and spintronics.