Related papers: Krylov subspace methods for the Dirac equation
Krylov subspace methods quantify operator growth in quantum many-body systems through Lanczos coefficients that encode how operators spread under time evolution. Although these diagnostics were originally motivated by questions of chaos and…
The low rank approximation of matrices is a crucial component in many data mining applications today. A competitive algorithm for this class of problems is the randomized block Lanczos algorithm - an amalgamation of the traditional block…
The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…
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…
The zero-temperature single-particle Green's function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding…
The solution of linear non-autonomous ordinary differential equation systems (also known as the time-ordered exponential) is a computationally challenging problem arising in a variety of applications. In this work, we present and study a…
We propose a two-sided Lanczos method for the nonlinear eigenvalue problem (NEP). This two-sided approach provides approximations to both the right and left eigenvectors of the eigenvalues of interest. The method implicitly works with…
We develop a block minimum residual (MINRES) algorithm for symmetric indefinite matrices. This version is built upon the band Lanczos method that generates one basis vector of the block Krylov subspace per iteration rather than a whole…
The Dirac oscillators are shown to be an excellent expansion basis for solutions of the Dirac equation by $R$-matrix techniques. The combination of the Dirac oscillator and the $R$-matrix approach provides a convenient formalism for…
We increase the efficiency of a recently proposed time integration scheme for time dependent quantum transport by using the Lanczos method for time evolution. We illustrate our modified scheme in terms of a simple one dimensional model. Our…
The computation of the Schr\"odinger equation featuring time-dependent potentials is of great importance in quantum control of atomic and molecular processes. These applications often involve highly oscillatory potentials and require…
In this article, we obtain the exact solutions for bound states of tilted anisotropic Dirac materials under the action of external electric and magnetic fields with translational symmetry. In order to solve the eigenvalue equation that…
We give a novel spectral approximation algorithm for the balanced separator problem that, given a graph G, a constant balance b \in (0,1/2], and a parameter \gamma, either finds an \Omega(b)-balanced cut of conductance O(\sqrt(\gamma)) in…
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…
The Lanczos method is one of the standard approaches for computing a few eigenpairs of a large, sparse, symmetric matrix. It is typically used with restarting to avoid unbounded growth of memory and computational requirements. Thick-restart…
This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial…
We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large,…
The ubiquitous Lanczos method can approximate $f(A)x$ for any symmetric $n \times n$ matrix $A$, vector $x$, and function $f$. In exact arithmetic, the method's error after $k$ iterations is bounded by the error of the best degree-$k$…
We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$. Let $A$ be an $n \times n$ Hermitian matrix. We show that when run for few iterations, the output of Lanczos on $A$ is almost…
This paper presents an efficient and concise double fast algorithm to solve high dimensional time-space fractional diffusion problems with spectral fractional Laplacian. We first establish semi-discrete scheme of time-space fractional…