Strongly Correlated Electron Systems: An Operatorial Perspective

We discuss the operatorial approach to the study of strongly correlated electron systems and show how the exact solution of target models on small clusters chosen ad-hoc (minimal models) can suggest very efficient bulk approximations. We use the Hubbard model as case study (target model) and we analyze and discuss the crucial role of spin fluctuations in its 2-site realization (minimal model). Accordingly, we devise a novel three-pole approximation for the 2D case, including in the basic field an operator describing the dressing of the electronic one by the nearest-neighbor spin-fluctuations. Such a solution is in very good agreement with the exact one in the minimal model (2-site case) and performs very well once compared to advanced (semi-)numerical methods in the 2D case, being by far less computational-resource demanding.