Related papers: Ground State and Finite Temperature Lanczos Method…
In this work, we consider the numerical computation of ground states and dynamics of single-component Bose-Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as…
The need for large-scale electronic structure calculations arises recently in the field of material physics and efficient and accurate algebraic methods for large simultaneous linear equations become greatly important. We investigate the…
In this article, new results are presented for the zero-temperature ground-state properties of the spin-half transverse Ising model on various lattices using three different approximate techniques. These are, respectively, the coupled…
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of…
New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose-Einstein condensates (BECs) described by a three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a dipolar interaction…
We present a Lanczos tau method for the approximation and optimization of the $H^2$-norm of time-delay systems described by semi-explicit delay differential algebraic equations. The soundness of this approach is proven under the assumption…
In theory, the Lanczos algorithm generates an orthogonal basis of the corresponding Krylov subspace. However, in finite precision arithmetic, the orthogonality and linear independence of the computed Lanczos vectors is usually lost quickly.…
Ground state of the dissipative two-state system is investigated by means of the Lanczos diagonalization method. We adopted the Hilbert-space-reduction scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming…
A common approach to approximating quadratic forms of matrix functions is to use a quadrature rule derived from the Lanczos process, known as a Lanczos quadrature. Although symmetric quadrature rules are computationally favorable, it has…
DMFT combined with finite-T exact diagonalization is one of the methods to describe electronic properties of strongly correlated materials. Because of the rapid growth of the Hilbert space, the size of the finite bath used to represent the…
This work considers large-scale Lyapunov matrix equations of the form $AX + XA = \boldsymbol{c}\boldsymbol{c}^T$, where $A$ is a symmetric positive definite matrix and $\boldsymbol{c}$ is a vector. Motivated by the need to solve such…
Two-dimensional coherent spectroscopy (2DCS) with terahertz radiation offers a promising new avenue for the exploration of many-body phenomena in quantum magnets. This includes the potential diagnosis of fractionalized excitations, for…
We consider the approximation of $B^T (A+sI)^{-1} B$ where $A\in\mathbb{R}^{n\times n}$ is large, symmetric positive definite, and has a dense spectrum, and $B\in\mathbb{R}^{n\times p}$, $p\ll n$. Our target application is the computation…
We show that the standard Lanczos algorithm can be efficiently implemented statistically and self consistently improved, using the stochastic reconfigurat ion method, which has been recently introduced to stabilize the Monte Carlo sign…
In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…
This work presents a new methodology for computing ground states of Bose-Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a pre-processing step, a low-dimensional (coarse)…
We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems. Focusing on autocorrelation functions of local operators and on their infinite-time behaviour at finite size, we conjecture that in…
Using Lanczos exact diagonalization (ED), we study the spin-1/2 $J_1$-$J_2$ Heisenberg model with the four-spin ring-exchange interaction $J_r$ on triangular lattice. We mainly use the level spectroscopic technique of two 36-site tori to…
A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…
In this work we describe a new technique for numerical exact diagonalization. The method is particularly suitable for cold bosonic atoms in optical lattices, in which multiple atoms can occupy a lattice site. We describe the use of the…