INVESTIGATING ESSENTIAL SPECTRA AND DISCRETE ENERGY LEVELS IN HUBBARD'S FIVE-ELECTRON MODEL

Abstract

In the early 1970s, seminal works by Hubbard and others introduced the Hubbard model, a fundamental theoretical construct for understanding strongly correlated electron systems. This model focuses on a nondegenerate electron band subjected to a local Coulomb interaction, encompassing only two key parameters: the electron hopping matrix element (t) between neighboring lattice sites and the on-site Coulomb repulsion (U) between electrons. The Hamiltonian of this model captures the essence of this description. This paper traces the historical development of the Hubbard model, which was named in honor of John Hubbard's pioneering contributions to its statistical mechanics analysis. Interestingly, the concept of local Coulomb interaction was initially introduced by Anderson in the context of impurity models in metals. Furthermore, it is essential to note that the Hubbard model is a specific instance of the Shubin-Wonsowsky polaron model, which predates it by three decades and extends the interaction to neighboring sites. The Hubbard model's simplicity, featuring only two terms in its Hamiltonian—kinetic tunneling and on-site interaction—renders it an invaluable tool in solidstate physics. It elegantly captures the transition from conducting to insulating states and accommodates both fermionic and bosonic particles. This model's effectiveness in describing strongly correlated electron systems has solidified its status as a cornerstone in condensed matter physics.