Abstract:
The Hubbard model ( H = -t Σ<i,j>,σ Cjσ† Ci,σ + U Σi ni,↑ ni,↓ ) is one of the most important model Hamiltonians for strongly correlated systems. It is the easiest model one can write that captures the essential physics of strongly correlated systems and is believed by many physicists to be a good starting point to studying the High Tc problem. The Hubbard model has two terms. One is a kinetic energy term, which describes electrons hopping between nearest neighbor sites and represents their "wave-like" behavior. The second term is due to Coulomb repulsion between electrons on the same site (potential energy) and represents the "particle-like" nature of electrons. Although the Hubbard model seems to be very simple, after more than 40 years since its introduction, we still do not know much about it and its physical properties. The Hubbard model seems to have many exotic and unusual properties because of the way it mixes both the wave and particle nature of electrons.
In this talk I am going to introduce a slave boson method that transforms the Hubbard model into a new form which is easier to work with, especially when "t" is comparable to "U," and is more useful for physical purposes. Then I will show that this form of the Hubbard model has U(1) gauge symmetry and can lead to d-wave superconductivity.Then I will discuss the connections between this model and other slave boson methods and I will talk about new possibilities due to this kind of slave boson. I will briefly discuss the Hubbard model's phase diagram based on the gauge theory of the Hubbard model. In the last part of my talk I will also introduce a gauge invariant trial wave-function which satisfies all constraints and has most of the desired properties. Then I will argue whether the mean field results using this trial wave-function are reliable or not. Finally I will show how one can get the phase diagram using this method.