Related papers: Analytical contradictions of the 'fixed - node' de…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
A semiclassical linear response theory based on the Vlasov equation is reviewed. The approach discussed here differs from the classical one of Vlasov and Landau for the fact that the finite size of the system is explicitly taken into…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
The presence of sharp peaks in the real part of the static dielectric response function are usually accepted as indication of charge or spin instabilities in a material. However, there are misconceptions that Fermi surface (FS) nesting…
We study the one-body reduced density matrix of a system of $N$ one-dimensional impenetrable anyons trapped by a harmonic potential. To this purpose we extend two methods developed to tackle related problems, namely the determinant approach…
Numerical simulations of strongly correlated electron systems suffer from the notorious fermion sign problem which has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we…
We examine the effective interaction of nonrelativistic fermions with an external vector field in superfluid systems. In contrast to the complicated vertex equation, usually used in this case, we apply the approach which does not employ an…
Numerical simulations of strongly correlated fermions at finite temperature are essential for studying high-temperature superconductivity and other quantum many-body phenomena. The recently developed tangent-space tensor renormalization…
We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling…
We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in…
We explore the structure of momentum distributions of Fermi liquids such as completely polarized 3He, unpolarized liquid 3He, and nuclear matter at nonzero temperatures. The study employs correlated density matrix theory and adapts the…
We study thermalization in a one-dimensional quantum system consisting of a noninteracting fermionic chain with each site of the chain coupled to an additional bath site. Using a density matrix renormalization group algorithm we investigate…
Exact and approximate expressions for thermodynamic characteristics of heated matter, which consists of particles with finite mass-widths, are constructed. They are expressed in terms of Fermi/Bose distributions and spectral functions,…
The aim of this thesis is to systematically and consistently study strongly coupled bosonic and fermionic conformal field theories using the large quantum number expansion. The idea behind it is to study sectors of conformal field theories…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
We systematically investigate the intricate interplay between short-range fermion-fermion interactions and disorder scatterings beneath the superconducting dome of noncentrosymmetric nodal-line superconductors. Employing the renormalization…
The renormalization group approach as developed by the author for Fermi liquids is applied to clean Fermi liquids and ballistic quantum dots. In the former case Landau theory is shown to be a fixed point and in the latter the Universal…
In recent years, a method for computing spin dynamics at infinite temperature (spinDMFT) was developed. It utilizes the ideas of dynamical mean-field theory for fermions: single-site approximation and a self-consistency condition to…