Related papers: On Born's conjecture about optimal distribution of…
The goal of this work is to investigate the optimality of the $d$-dimensional rock-salt structure, i.e., the cubic lattice $V^{1/d}\mathbb{Z}^d$ of volume $V$ with an alternation of charges $\pm 1$ at lattice points, among periodic…
We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice…
To investigate the possibility of charge order and superconductivity in a doped two-dimensional triangular lattice, we study the extended Hubbard model with variational Monte Carlo method. At n=2/3, a commensurate filling for a triangular…
Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended…
We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be convex, and the criterion is to minimize either the sum or the maximum among the…
We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has honeycomb geometry with a staggered energy-offset that explicitly breaks the…
We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of…
We study the quantum phase transition between a band (``ionic'') insulator and a Mott-Hubbard insulator, realized at a critical value U=Uc in a bipartite Hubbard model with two inequivalent sites, whose on-site energies differ by an offset…
The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated…
The Born effective charges of component atoms and phonon spectra of a tetrahedrally coordinated crystalline ice are calculated from the first principles method based on density functional theory within the generalized gradient approximation…
We revisit the spectral problem for Bloch electrons in a two-dimensional bipartite honeycomb lattice under a uniform magnetic field. It is well-known that such a honeycomb structure is realized in graphene. We present a systematic framework…
Using a non-contact atomic force microscope (nc-AFM), we examine continuous DB wire structures on the hydrogen-terminated silicon (100) 2x1 surface. By probing the DB structures at varying energies, we identify the formation of previously…
We consider the extended half-filled Hubbard model on the honeycomb lattice for second nearest neighbors interactions. Using a functional integral approach, we find that collective fluctuations suppress topological states and instead favor…
In this paper, we focus on finite Bravais lattice energies per point in two dimensions. We compute the first and second derivatives of these energies. We prove that the Hessian at the square and the triangular lattice are diagonal and we…
We consider the minimizing problem for energy functionals with two types of competing particles and completely monotone potential on a lattice. We prove that the minima of sum of two completely monotone functions among lattices is located…
We investigate the minimization of the energy per point $E\_f$ among $d$-dimensional Bravais lattices, depending on the choice of pairwise potential equal to a radially symmetric function $f(|x|^2)$. We formulate criteria for minimality and…
We develop a method of variational optimization of the infinite projected entangled pair states on the honeycomb lattice. The method is based on the automatic differentiation of the honeycomb-lattice corner transfer matrix renormalization…
The amorphous propagation of microstructures during the electrochemical charging of a battery is the main reason for the capacity decay and short circuit. The charge distribution across the micro-structure is the result of both local and…
We obtain the most general forms of rank-2 and rank-3 tensors allowed by the crystal symmetries of the honeycomb lattice of edge-sharing octahedra for crystals belonging to different crystallographic point groups, including the monoclinic…
We present here novel insight into exchange-correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the semiclassical limit, the exact…