Analysis of thermodynamic quantities in the Hubbard model by means of the Composite Operator Method

The electronic states of the two-dimensional Hubbard model are investigated by means of a 4-pole approximation within the Composite Operator Method. In addition to the conventional Hubbard operators, we consider other two operators which come from the hierarchy of the equations of motion. These operators carry information regarding surrounding spin and charge configurations. In the study of thermodynamic quantities, such as internal energy and specific heat, our results present an excellent agreement with the data of numerical simulation. Furthermore, in the low-temperature region, they show a decrease of energy suggesting spin and charge ordering which cannot be well evaluated by the former 2-pole approximation.