Related papers: Bloch's theorem in orbital-density-dependent funct…
An analytic solution of the Hartree-Fock problem for a 2DEG at filling 1/3 and half an electron per unit cell is presented. The Coulomb interaction dynamically breaks the first Landau level in three narrow sub-bands, one of which is fully…
It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion…
We study the transformation properties of the electron states in crystals with spin-orbit coupling, focusing primarily on the limitations of the frequently used pseudospin-1/2 description of twofold degenerate Bloch bands. Using the…
We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
Our electronic structure theory for crystalline solids is commonly built on the periodic potential assumption $V(\mathbf r)=V(\mathbf r+\mathbf R)$ for every lattice translation $\mathbf R$, enabling Bloch eigenstates, crystal momentum as a…
With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of…
We investigate the infinite-dimensional two-orbital Hubbard model at arbitrary band fillings. By means of the self-energy functional approach, we discuss the stability of the metallic state in the systems with same and different bandwidths.…
Using a general analytical continuation scheme for cluster dynamical mean field calculations, we analyze real-frequency self-energies, momentum-resolved spectral functions, and one-particle excitations of the metallic and insulating phases…
For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For…
Electronic bands in crystals are described by an ensemble of Bloch wave functions indexed by momenta defined in the first Brillouin Zone, and their associated energies. In an insulator, an energy gap around the chemical potential separates…
Spectral properties of periodic one-dimensional array of nanorings in a magnetic field are investigated. Two types of the superlattice are considered. In the first one, rings are connected by short one-dimensional wires while in the second…
We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band…
Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the…
Functionally graded materials (FGMs) are composites whose composition or microstructure varies continuously in space, producing position-dependent mechanical and functional properties. In recent years, FGMs have gained significant attention…
Tetragonal phase of CuMnAs progressively appears as one of the key materials for antiferromagnetic spintronics due to efficient current-induced spin-orbit torques whose existence can be directly inferred from crystal symmetry. Theoretical…
The construction of Hilbert spaces that are characterized by local constraints as the low-energy sectors of microscopic models is an important step towards the realization of a wide range of quantum phases with long-range entanglement and…
Koopman operator, as a fully linear representation of nonlinear dynamical systems, if well-defined on a reproducing kernel Hilbert space (RKHS), can be efficiently learned from data. For stability analysis and control-related problems, it…
The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review…
We examine spectral operator-theoretic properties of linear and nonlinear dynamical systems with globally stable attractors. Using the Kato Decomposition we develop a spectral expansion for general linear autonomous dynamical systems with…