New Formalism for Determining Excitation Spectra of Many-Body Systems

Orlando, Roberto

The subject of the thesis focuses on new approximations studied in a formalism based on a perturbation theory allowing to describe the electronic properties of many-body systems in an approximate way. We excite a system with a small disturbance, by sending light on it or by applying a weak electric field to it, for example and the system "responds" to the disturbance, in the framework of linear response, which means that the response of the system is proportional to the disturbance. The goal is to determine what we call the neutral excitations or bound states of the system, and more particularly the single excitations. These correspond to the transitions from the ground state to an excited state. To do this, we describe in a simplified way the interactions of the particles of a many-body system using an effective interaction that we average over the whole system. The objective of such an approach is to be able to study a system without having to use the exact formalism which consists in diagonalizing the N-body Hamiltonian, which is not possible for systems with more than two particles.

Philippe H. Monthoux, Efstratios Manousakis

Li, Hui

A fundamental challenge in quantum many-body physics is to understand the universal properties of strongly correlated systems. In this work, we establish a universal and exact identity from the Dyson-Schwinger equations within the Keldysh-Schwinger field theory for systems with generic bilinear interactions. Our derivation demonstrates the emergence of composite particles as "elementary excitations", whose Green's functions definitively determine the original single-particle Green's function. This universal relation uniquely identifies the composite particles governing correlations and rigorously connects their spectra to the observable single-particle spectrum. Thus, our exact identity reveals a new pathway toward a paradigm for understanding many-body correlated systems.

F. Bechstedt

Theo A. Costi, Alex C. Hewson

Filip Filipović

This thesis deals with the determination of the eigenstates of the Hamiltonian and quantum dynamics in many-body interacting systems. As an example, the Bose- Hubbard model is used. Methods of generating the basis of system state space and calculation of Hamiltonian matrix in selected representations are studied. After the complete specification of the system, the energy spectrum and the eigenstates are determined. By using the appropriate techniques, the mapping of the vector index and quantum numbers is established for efficient access and manipulation for physical quantities evaluations and simulating dynamics in quantum interacting systems. Furthermore, the expected distribution of particles and momenta are examined, studying the behaviour of characteristic quantities such as energy gaps, the excitation spectra of such a system as a function of the Hamiltonian parameters is determined for a couple of cases. An overview of the formalism of second quantization is given in the paper as well as the derivation of the Bose-Hubbard model in this formalism. Also, the limit of infinitely strong repulsive interactions between the bosons is investigated when the system shows certain similarities with the system of non-interacting fermions onto which it is mapped. In the end, the time evolution of the system of bosons in an optical lattice is investigated in the presence of an external potential in the case of a constant and a time-varying potential.