This book reports on research in a field of prominence in modern theoretical and experimental physics, namely the understanding and characterization of many-body phenomena in condensed matter systems where interactions among electrons play a fundamental role. A thorough assessment of a pre-existing method to quantify theoretical approach for low-dimensional systems is performed. The procedure to such method is implemented and used to predict the electrical response to an external electric field of finite 1D chains. This is relevant not just as a test of the method but also for understanding real materials, whose electrical response can be mimicked in terms of Hubbard model. The 1D case, in particular, can provide important insights into the nonlinear optical properties of polymers. Additionally, this book introduced and implemented a novel extension of the existing method in magnetic field. This is successfully applied to investigating magnetic properties of systems involving large ensemble averages. It also investigates the magnetic behavior of several systems using the computationally efficient atomic self-interaction correction scheme in density functional theory.