相关论文: Chebyshev Matrix Product State Impurity Solver for…

A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum…

We present the combination of a complex-time tensor-network impurity solver with an analytic continuation scheme based on exponential fitting as an efficient framework for single and multi-orbital dynamical mean-field calculations. By…

Density Functional Tight Binding (DFTB) is an attractive method for accelerated quantum simulations of condensed matter due to its enhanced computational efficiency over standard Density Functional Theory approaches. However, DFTB models…

As in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is…

Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…

This paper develops a computational method for studying stable/unstable manifolds attached to periodic orbits of differential equations. The method uses high order Chebyshev-Taylor series approximations in conjunction with the…

Deep unfolding is a promising deep-learning technique, whose network architecture is based on expanding the recursive structure of existing iterative algorithms. Although convergence acceleration is a remarkable advantage of deep unfolding,…

We provide a mathematical analysis of the Dynamical Mean-Field Theory, a celebrated representative of a class of approximations in quantum mechanics known as embedding methods. We start by a pedagogical and self-contained mathematical…

We introduce and analyze a mesh-free two-level hybrid Chebyshev-Tucker tensor representation for approximating multivariate functions, which combines tensor-product Chebyshev interpolation with the low-rank Tucker decomposition of the…

Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their…

Renormalization Group (RG) theory provides the theoretical framework to define Effective Theories (ETs), i.e. systematic low-resolution approximations of arbitrary microscopic models. Markov State Models (MSMs) are shown to be rigorous ETs…

We improve the methodology to construct a complete active space-configuration interaction (CAS-CI) expansion for density-matrix renormalization group (DMRG) wave function using matrix-product state representation, inspired by the…

Both unconstrained and constrained minimax single facility location problems are considered in multidimensional space with Chebyshev distance. A new solution approach is proposed within the framework of idempotent algebra to reduce the…

A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral…

We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce…

A dynamic mixed super-resolution model (DMSRM) for large-eddy simulations (LESs) is proposed, which combines the traditional dynamic mixed model (DMM) formulation with the generation of super-resolved velocity fields from which the…

A zero-site density matrix renormalization algorithm (DMRG0) is proposed to minimize the energy of matrix product states (MPS). Instead of the site tensors themselves, we propose to optimize sequentially the "message" tensors between…

Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp.,…

We propose an initialization procedure for the density-matrix renormalization group (DMRG): {\it the recursive sweep method}. In a conventional DMRG calculation, the infinite-algorithm, where two new sites are added to the system at each…

We implement the recently developed influence functional matrix product states approach as impurity solver in equilibrium and nonequilibrium dynamical mean field theory (DMFT) calculations of the single-band Hubbard model. The method yields…