Renormalized theory of the two-dimensional S=1/2S=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≠0T≠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≠0T≠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=0T=0 and T>0T>0. We think that our renormalization scheme is a more general and systematic approach in condensed matter physics.