Renormalized theory of the two-dimensional S=1/2 dilute spin-wave systems at low temperatures

Due to strong fluctuations, conventional approaches to handling repulsive spin-1/2 spin-waves in three dimensions do not work in low dimensions at temperature T≠0. We have constructed a renormalized theory for the two-dimensional spin-1/2 anisotropic quantum Heisenberg model by means of exact mappings between spin-1/2 systems and their corresponding hard-core Bose-Hubbard systems. With the t-matrix method, hard-core Bose-Hubbard systems can be effectively described by the corresponding soft-core Bose-Hubbard Hamiltonians at low energy. The method of running coupling constant in field theory is used to fix the infrared divergence due to long wavelength fluctuations in low dimensions at T≠0. Our results agree well with previous analytical and numerical works. The method dealing with infinities used by others in 3D is a special case of our renormalization scheme. Our approach works in both two and three dimensions at T=0 and T>0. We think that our renormalization scheme is a more general and systematic approach in condensed matter physics