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Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the…
LDA+DMFT, the computation scheme merging the local density approximation and the dynamical mean-field theory, is employed to calculate spectra both below and above the Fermi energy and spin and orbital occupations in the correlated…
Network embedding, a graph representation learning method illustrating network topology by mapping nodes into lower-dimension vectors, is challenging to accommodate the ever-changing dynamic graphs in practice. Existing research is mainly…
Detailed analysis of the magnetic properties of the Hubbard model within dynamical mean-field theory (DMFT) is presented. Using a RPA-like decoupling of two-particle propagators we derive a universal form for susceptibilities, which…
To understand the essential physics needed to reproduce magnetic reconnection events in 2.5-D particle-in-cell (PIC) simulations, we revisit the Geospace Environmental Modeling (GEM) setup. We set up a 2-D Harris current sheet (that also…
We compare different approximation schemes for investigating ferromagnetism in the periodic Anderson model. The use of several approximations allows for a detailed analysis of the implications of the respective methods, and also of the…
In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital…
We review the basic ideas of the dynamical mean field theory (DMFT) and some of the insights into the electronic structure of strongly correlated electrons obtained by this method in the context of model Hamiltonians. We then discuss the…
Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for…
The stationary functional of the all-electron density functional plus dynamical mean field theory (DFT+DMFT) formalism to perform free energy calculations and structural relaxations is implemented for the first time. Here, the first order…
Density functional theory (DFT) is a widespread and effective tool in electronic structure calculations for ground-state electron systems. Its success has prompted exploration into the use of DFT for non-collective excited states. The delta…
We present an accurate local density-functional for electronic-structure calculations within the density functional theory (DFT). The functional is derived by analyzing the structure of the standard perturbative expansion of the correlation…
We continue our exploration of local Double Field Theory (DFT) in terms of symplectic graded manifolds carrying compatible derivations and study the case of heterotic DFT. We start by developing in detail the differential graded manifold…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
For a matrix ${\bf A}$ with linearly independent columns, this work studies to use its normalization $\bar{\bf A}$ and ${\bf A}$ itself to approximate its orthonormalization $\bf V$. We theoretically analyze the order of the approximation…
We present a theoretical study of the magnetic phase diagram of the frustrated coupled ladder structure realized recently in several materials. This system displays a nondegenerate spin-gap state in the dimer limit and an infinitely…
The study of strongly correlated electron systems remains a fundamental challenge in condensed matter physics, particularly in two-dimensional (2D) systems hosting various exotic phases of matter including quantum spin liquids,…
We present a dynamical model that successfully explains the observed time evolution of the magnetization in diluted magnetic semiconductor quantum wells after weak laser excitation. Based on the pseudo-fermion formalism and a second order…
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…
We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group…