Related papers: Variational exact diagonalization method for Ander…
Predicting the properties of strongly correlated materials is a significant challenge in condensed matter theory. The widely used dynamical mean-field theory faces difficulty in solving quantum impurity models numerically. Hybrid…
This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
By means of a projector-operator formalism we derive an approximation based on a self consistent hybridization expansion to study the ground state properties of the Anderson Impurity model. We applied the approximation to the general case…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
We propose a general strategy for solving nonlinear integro-differential evolution problems with periodic boundary conditions, where no direct maximum/minimum principle is available. This is motivated by the study of recent macroscopic…
Using exact diagonalizations we consider self-consistently the lattice distortions in odd Peierls-Hubbard and spin-Peierls periodic rings in the adiabatic harmonic approximation. From the tails of the inherent spin soliton the dimerization…
An exactly solvable one-dimensional Hubbard model with a single Anderson impurity embedded at the boundary is constructed in the framework of the quantum inverse scattering method. The model is solved exactly by the nested Bethe ansatz…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
The Anderson impurity model (AIM) is of fundamental importance in condensed matter physics to study strongly correlated effects. However, accurately solving its long-time dynamics still remains a great numerical challenge. An emergent and…
We present a new variational model for computing the electronic first-order density matrix of a crystalline material in presence of a local defect. A natural way to obtain variational discretizations of this model is to expand the…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…
We develop a diagrammatic Monte Carlo method for the real-time dynamics of dissipative quantum impurity models. These are small open quantum systems with interaction and local Markovian dissipation, coupled to a large quantum bath. Our…
We present a powerful method for calculating the thermodynamic properties of the Hubbard model in infinite dimensions, using an exact diagonalization of an Anderson model with a finite number of sites. At finite temperatures, the explicit…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…