Related papers: The Hubbard model: basic notions and selected appl…
First applications of the new algorithm simulating dynamical fermions are reported. The method reproduces previous results obtained with different techniques.
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…
There are few exact results for the Hubbard model on bipartite lattices of spatial dimension $d>1$. Nevertheless, the Hubbard model with transfer integral $t$ and onsite repulsion $U$ on bipartite lattices with $N_a$ sites, such as the…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The relation with the "classical" Hamiltonian approach using canonical transformations is also…
Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an…
We reconsider the quantum inverse scattering approach to the one-dimensional Hubbard model and work out some of its basic features so far omitted in the literature. It is our aim to show that $R$-matrix and monodromy matrix of the Hubbard…
This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…
The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the `standard model' of condensed matter physics. The model has been remarkably…
Paper: cond-mat/9311033 The Hubbard model of interacting electrons, like the Ising model of spin-spin interactions, is the simplest possible model displaying many ``real world'' features, but it is much more difficult to analyze…
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…
The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, towards efficient quantum computing of molecular electronic structure calculations.…
We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…
This is a short introduction to Hilbert space frame theory and its applications for those outside the area who want to enter the subject. We will emphasize finite frame theory since it is the easiest way to get into the subject.
The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical…