Related papers: Ground states for aggregation-diffusion models on …
Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other…
We present a complete derivation of two-particle states of the one-dimensional extended Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and…
We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…
We study an attractive Hubbard model on bipartite lattices. In the grand canonical formalism,we prove the existence of superconducting long-range order in the ground state on Lieb lattices with the chemical potential corresponding to half…
We investigate the competition between attractive spin-spin interactions and spin-separating external forces in the ground state of a one-dimensional Fermi-Hubbard model. We consider a lattice with open boundary conditions, subject to a…
Within the frame of lowest-order perturbation theory, the van der Waals potential of a ground-state atom placed within an arbitrary dispersing and absorbing magnetodielectric multilayer system is given. Examples of an atom situated in front…
We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < \infty$. We first prove the existence of possibly infinitely many…
We generalize the linear discrete dimensional scaling approach for the repulsive Hubbard model to obtain a nonlinear scaling relation that yields accurate approximations to the ground-state energy in both two and three dimensions, as judged…
A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…
A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the possible occurrence of a bound state is perhaps the most…
We study properties of energy spreading in a lattice of elastically colliding harmonic oscillators (Ding-Dong model). We demonstrate that in the regular lattice the spreading from a localized initial state is mediated by compactons and…
We discuss the behavior of the entanglement entropy of the ground state in various collective systems. Results for general quadratic two-mode boson models are given, yielding the relation between quantum phase transitions of the system…
The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems.…
We consider the mass-critical nonlinear Schr\"odinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass…
In this article, we consider fixed spin 1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give some asymptotic expansions for the ground state and the ground state energy of the…
We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction U < 0 using the density matrix renormalization group method as well as a perturbation theory. We find that…
We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a…
We study the phase stability of the Edwards-Anderson spin-glass model by analyzing the domain-wall energy. For the bimodal distribution of bonds, a topological analysis of the ground state allows us to separate the system into two regions:…
We study the ground state energy of a gas of $N$ fermions confined to a unit box in $d$ dimensions. The particles interact through a 2-body potential with strength scaled in an $N$-dependent way as $N^{-\alpha}v$, where $\alpha\in \mathbb…