Related papers: Absence of Luttinger's Theorem due to Zeros in the…
Interactions between electrons in one-dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model which is based on linearisation of the spectrum. We consider a model of spinless fermions with a…
Using the Green's function method, we study the effect of an impurity potential on the electronic structure of the honeycomb lattice in the one-band tight-binding model that contains both the nearest neighbor ($t$) and the second neighbor…
Self-consistent approaches in many-electron problems typically converge to an unphysical solution in strongly correlated regimes. By deriving the mathematical condition for the stability of the physical solution, we unveil the precise…
We study global anomalies of nonlocal effective theories proposed to describe symmetry-preserving Luttinger surfaces, i.e., the momentum-space manifolds of Green's function zeros (GFZs) at zero energy, in strongly interacting fermionic…
In this Ph.D. thesis a model for graphene in presence of quantized electromagnetic interactions is introduced. The zero and low temperature properties of the model are studied using rigorous renormalization group methods and lattice Ward…
It is known that, under short-range interactions many topological superconductors (TSC) and topological insulators (TI) are trivialized, which means the boundary state of the system can be trivially gapped out by interaction without leading…
The retarded Green function of a wave equation on a 4-dimensional curved background spacetime is a (generalized) function of two spacetime points and diverges when these are connected by a null geodesic. The Hadamard form makes explicit the…
We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle…
The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of quantum mechanics, and constitutes the basis for the very successful density-functional approach to inhomogeneous interacting many-particle systems. Here we show…
We show that the $N$-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the $N$-body ground state wave functions with two…
We investigate analytically the performance of many-body energy functionals, derived respectively by Klein and Luttinger and Ward, at different levels of diagrammatic approximations, ranging from second Born, to GW, to the so-called…
We have postulated a single pole for the self-energy, $\Sigma(\vec{k},\omega)$, looking for the consequences on the one-particle Green function, $G(\vec{k},\omega)$ in the Hubbard model. We find that $G(\vec{k},\omega)$ satisfies the first…
The method of the quasiclassical Green's function is used to determine the equilibrium properties of one-dimensional (1D) interacting Fermi systems, in particular, the bulk and the local (near a hard wall) density of states. While this is a…
We obtained the analog of the Luttinger relation for a commensurate spin-density-wave state. We show that while the relation between the area of the occupied states and the density of particles gets modified in a simple and predictable way…
A perturbation theory scheme in terms of electron hopping, which is based on the Wick theorem for Hubbard operators, is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each…
It is shown that the Hohenberg-Kohn lemma and theorem are direct consequences of the statement that the ground state energy (or free energy) of a system of interacting particles in an external field is a unique functional of the potential…
We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward Identities. At the critical temperature, T = 0, the…
We solve the Dyson equation for atoms and diatomic molecules within the GW approximation, in order to elucidate the effects of self-consistency on the total energies and ionization potentials. We find GW to produce accurate energy…
The effect of a randomly fluctuating gap, created by a random staggered potential, is studied in a monolayer and a bilayer of graphene. The density of states, the one-particle scattering rate and transport properties (diffusion coefficient…
When a local potential changes abruptly in time, an electron gas shifts to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson's orthogonality catastrophe and it is…