Sharif Digital Repository

Non-equilibrium systems refer to systems in which, unlike equilibrium systems, the initial condition plays an important role. Conventional methods in quantum field theory cannot be used to study these systems because they do not necessarily have a convergent perturbative expansion.In this thesis, we first briefly introduce the Ising model and fermions in the lattice gauge theory. We then introduce the two-particle irreducible (2PI) method as a tool to investigate nonequilibrium systems. Finally, using this method, we reformulate the Ising model for a system out of equilibrium  

Out-of-equilibrium systems have garnered increasing interest in recent years. These many-body systems do not exhibit ergodic behavior, even in the presence of generic interactions, allowing locally stored quantum information to remain accessible for extended periods through local observables. Due to these exotic characteristics, such systems are ideal candidates for the realization of quantum computing. Many-body localized systems serve as a prime example of these non-ergodic systems. In the absence of thermalization, long-range quantum order can persist even in highly excited states, contrasting with thermal systems where long-range order can only exist in the ground state of gapped... 

In this thesis we put forward a new theoretical framework that combines the LuttingerWard (LW) functional methodology with a slave-rotor construction. As such, the strongly correlated electronic problem is systematically mapped onto a weakly coupled system of two primary excitations: spinons and chargons. In this projective construction, the electronic degrees of freedom are fractionalized, thereby enabling the study of emergent phenomena in a more tractable manner. Starting from the Hubbard model defined on a triangular lattice, two computational approaches are developed and lead to self-consistent equations for the Green’s functions. The first approach is based on Hartree-Fock...