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Quantum Rabi model (QRM) is widely used for the analysis of the radiation-matter interaction at the fundamental level in cavity quantum electrodynamics. Typically the QRM Hamiltonian includes only $\boldsymbol{\mathsf{p}} \cdot…
The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a…
Within the 1D Hubbard model linear closed chains with various numbers of sites are considered in Self Consistent Random Phase Approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for 2+4n sites cases,…
Self-consistent solutions of Hedin's diagrammatic theory equations (HE) for the two-site Hubbard Model (HM) have been studied. They have been found for three-point vertices of increasing complexity ($\Gamma=1$ (GW approximation),…
A systematic comparison is conducted for pairing properties of finite systems at nonzero temperature as predicted by the exact solutions of the pairing problem embedded in three principal statistical ensembles, as well as the unprojected…
A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find…
Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms,…
In this work, we calculate the matrix elements of $0\nu\beta\beta$-decay of $^{150}$Nd with the deformed pn-QRPA method. We adopted the approach introduced by Rodin, Faessler [Phys. Rev. C84, 014322 (2011)] and Simkovic {\it et. al.} [Phys.…
A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…
Neutrinoless double-beta ($0\nu\beta\beta$) decay and the standard two-neutrino double-beta ($2\nu\beta\beta$) decay of $^{98}$Mo have been studied. The double-beta decay $Q$-value has been determined as $Q_{\beta\beta}=113.668(68)$ keV…
We develop a concrete theory of continuous stripe melting quantum phase transitions in two dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in…
Understanding the behavior of non-Fermi liquids (NFLs) is an important topic in condensed matter physics. Here we introduce an exactly solvable multi-orbital model based on iron oxypnictides and the Hatsugai-Kohmoto model, and provide exact…
Background: To access selected excited states of nuclei, within the framework of nuclear density functional theory, the quasiparticle random phase approximation (QRPA) is commonly used. Purpose: We present a computationally efficient, fully…
$\beta$-decay properties of nuclei are investigated within the relativistic nuclear energy density functional framework by varying the temperature and density, conditions relevant to the final stages of stellar evolution. Both thermal and…
Using the Bethe ansatz analysis as was reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly…
We construct a previously unknown $E_2$-quasi-exactly solvable non-Hermitian model whose eigenfunctions involve weakly orthogonal polynomials obeying three-term recurrence relations that factorize beyond the quantization level. The model…
In this thesis, the quantum Hamilton Jacobi (QHJ) formalism is used to study various exactly solvable (ES) and quasi -exactly solvable (QES) models. Using this method, we obtain the bound state eigenvalues and the eigenfunctions for the…
We address the problem of the Fermi surface renormalization and the quantum confinement regime (QCR) in the two coupled chains model(TCCM) of spinless fermions. We perform a self-consistent calculation of the renormalization group(RG) flows…
The application of the Correlated basis function theory and of the Fermi hypernetted chain technique, to the description of the ground state of medium-heavy nuclei is reviewed. We discuss how the formalism, originally developed for…
The study of neutrino-nucleus scattering processes is important for the new generation neutrino experiments for better understanding of the neutrino oscillation phenomenon. A significant source of uncertainty in the cross-section comes from…