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

摘要

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 softcore 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.