Introduction

                In the study of solid-state physics, many models have been developed for the analysis, and study of various material properties.  For example, the Heisenberg model, Hubbard model, t-J model, ...etc. which can easily be found in most of the condensed-matter-physics books or the solid-state-physics books. All these models are used to deal with the many-body problems, and the mathmatical formulations are all utilize second-quantized operators' language. Since the number of particles in a many-body problem is usually large, it would be nice to have a computer program to handle such calculation.

                Therefore, the main idea of this project is to provide the users a convenient tool for calculations involving the second-quantized operators.  The basis of this application are the algebra of Hubbard operators, because all the other operators, such as spin operators, Fermion operators, and Boson operators can be represented by Hubbard operators. By including the header files in the library, the users can use some special notations, which will be intordued below, to represent Hubbard operators in their own program. 

                Although this introduction priamarily involves "solid-state physics", the program is not only designed for those who study in this field.  As second quantization operators find broad use in many sub-fields of physics, these methods may also be adapted for more versatile use.  Users may conveniently define their own Hubbard operators with the same/similar algorithm, for use in any purpose that they wish.

                The application for Bose operators will not be introduced, since it is very easy to constuct. However, when applied to Bosons, the largest number of particles is finite in a computer simulation, which means that the definition of local states cannot be summed over an infinite number of particles. This leades to a change of the properties of the commutators; i.e. the coefficient of the lowest energy state will be different. This is quite natural for a "real" physical problem, since in reality the ideal Bose gas is a simplified model, and the interparticle interactions are important in actuality. 

Definition of Hubbard Operator

Fermion Operator -> Hubbard Operator

Spin Operator -> Hubbard Operator

Program Notation

Play-Ground  ( background knowledge )

References

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