Related papers: Fulop-Tsutsui interactions on quantum graphs
Recently it has been proposed that, in the framework of quantum field theory, both the Standard Model gauge and Yukawa interactions arise from a single gauge interaction in higher dimensions with supersymmetry. This leads to the unification…
Pseudogap is a ubiquitous phenomenon in strongly correlated systems such as high-$T_{\rm c}$ superconductors, ultracold atoms and nuclear physics. While pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional…
Pseudogap physics in strongly correlated systems is essentially scale dependent. We generalize the dynamical mean field theory (DMFT) by including into the DMFT equations dependence on correlation length of pseudogap fluctuations via…
The one electron spectral functions for the Luttinger model are discussed for large but finite systems. The methods presented allow a simple interpretation of the results. For finite range interactions interesting nonunivesal spectral…
We present a finite-size scaling analysis of the entanglement in a two-dimensional arrays of quantum dots modeled by the Hubbard Hamiltonian on a triangular lattice. Using multistage block renormalization group approach, we have found that…
We consider a class of ground states for quantum spin chains on an integer lattice. First we show that presence of the spectral gap between the ground state energy and the rest of spectrum implies the split property of certain subsystems.As…
A scheme is presented for realizing frequency-up conversion and a two-qubit quantum swap gate for intracavity fields. In the scheme, a V-type atomic ensemble prepared in their ground states collectively mediates the interaction between the…
To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we…
We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a…
We give examples of minimal extensions of the simplest SU(5) SUSY-GUT in which all squarks and sleptons of a family have different tree level masses at the unification scale. This phenomenon is general; it occurs when the quarks and leptons…
We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the four-fermion bulk interaction in detail. Using bosonization and vertex…
We consider possible superconducting instabilities in a two-dimensional Fermi system with short-ranged repulsive interactions between electrons. The possibility of an unusual superconducting paring due to the Kohn-Luttinger mechanism is…
We prove an approximation result showing how operators of the type $-\Delta -\gamma \delta (x-\Gamma)$ in $L^2(\mathbb{R}^2)$, where $\Gamma$ is a graph, can be modeled in the strong resolvent sense by point-interaction Hamiltonians with an…
We present a \emph{new} formulation of perturbation theory for quantum systems, designated here as: `mean field perturbation theory'(MFPT), which is free from power-series-expansion in any physical parameter, including the coupling…
In this Thesis, we study the behavior of spectral curves of quantum graphs under certain families of vertex conditions, called the $\delta_s$ family, which we define in this work. We focus on studying two main quantities related to the…
We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction…
These lecture notes bridge a gap between introductory quantum field theory (QFT) courses and state-of-the-art research in scattering amplitudes. They cover the path from basic definitions of QFT to amplitudes relevant for processes in the…
Recent experiments involving tilted graphene samples have shown evidence of a continuous phase transition in the $\nu=0$ quantum Hall bulk state. We present here a simple model that supports such a transition. In addition to a long range…
In this paper, I calculate the large $N$ limit of marginal $O(N)$ models with non-polynomial potentials in arbitrary odd dimensions $d$. This results in a new class of interacting pure conformal field theories (CFTs) in $d=3+4n$ for any $n…
We consider the many-body ground state of polarized fermions interacting via zero-range $\mathfrak{p}$-wave forces in a one-dimensional geometry. We rigorously prove that in the limit of infinite attractions spectral properties of any-order…