Related papers: Lanczos, the transfer matrix, and the signal-to-no…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we…
We investigate the electron-energy loss spectrum of one-dimensional undoped CuO$_{3}$ chains within an extended multi-band Hubbard model and an extended one-band Hubbard model, using the standard Lanczos algorithm. Short-range intersite…
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…
We suggest a method to compute approximations to temporal correlation functions of few-body observables in chaotic many-body systems in the thermodynamic limit based on the respective Lanczos coefficients. Given the knowledge of these…
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…
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…
Maxwell's equations are cast in the form of the Schr\"{o}dinger equation. The Lanczos propagation method is used in combination with the fast Fourier pseudospectral method to solve the initial value problem. As a result, a time-domain,…
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.…
The present review will focus on recent development of exact-diagonali- zation (ED) methods that use Lanczos algorithm to transform large sparse matrices onto the tridiagonal form. We begin with a review of basic principles of the Lanczos…
Lattice Quantum Chromodynamics (QCD) has significantly contributed to our understanding of the CKM matrix through precise determinations of hadronic matrix elements. With advancements in theoretical methodologies and computational…
The Lorentz Integral Transform (LIT) method is reformulated via the Lanczos algorithm both for inclusive and exclusive reactions. The new technique is tested for the total photoabsorption cross section of 3H and 4He. Due to the rapid…
The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear…
Lattice fermions with suppressed high momentum modes solve the ultraviolet slowing down problem in lattice QCD. This paper describes a stochastic evaluation of the effective action of such fermions. The method is a based on the Lanczos…
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal…
With the ongoing experimental interest in exploring the excited hadron spectrum, evaluations of the matrix elements describing the formation and decay of such states via radiative processes provide us with an important connection between…
We present an algorithm to compute Green's functions on quantum computers for interacting electron systems, which is a challenging task on conventional computers. It uses a continued fraction representation based on the Lanczos method,…
It is shown that the lowest excitation energies of a quantum many-fermion system in the random phase approximation (RPA) can be obtained by minimizing an effective classical energy functional. The minimum can be found very efficiently using…
A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…
We report an implementation of the recursion method that addresses quantum many-body dynamics in the nonperturbative regime. The method essentially amounts to constructing a Lanczos basis in the space of operators and solving coupled…