Related papers: Lanczos, the transfer matrix, and the signal-to-no…
We describe a further development of the stochastic state selection method, a new Monte Carlo method we have proposed recently to make numerical calculations in large quantum spin systems. Making recursive use of the stochastic state…
We improve the convergence of the Lanczos algorithm using the matrix product state representation. As an alternative to the density matrix renormalization group (DMRG), the Lanczos algorithm avoids local minima and can directly find…
We investigate the oblique Lanczos method recently put forward in arXiv:2406.20009 for analysing Euclidean correlators in lattice field theories and show that it is analytically equivalent to the well known Prony Generalised Eigenvalue…
Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the…
Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step,…
The ground state magnetic phase diagram of the one-dimensional quantum compass model (QCM) is studied using the numerical Lanczos method. A detailed numerical analysis of the low energy excitation spectrum is presented. The energy gap and…
Models of quantum systems scale exponentially with the addition of single-particle states, which can present computationally intractable problems. Alternatively, quantum computers can store a many-body basis of $2^n$ dimensions on $n$…
We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long, {\it et al.} [Phys. Rev. B {\bf 68}, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The…
Maxwell's equations for electrodynamics of dispersive and absorptive (passive) media are written in the form of the Schr\"odinger equation with a non-Hermitian Hamiltonian. The Lanczos time-propagation scheme is modified to include…
Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs) of nuclear effective field theories (EFTs) from first-principles calculations that incorporate the dynamics of quarks and gluons. Given the…
This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical…
We establish rigourously the scaling properties of the Lanczos process applied to an arbitrary extensive Many-Body System which is carried to convergence n to infinity and the thermodynamic limit N to infinity taken. In this limit the…
Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulting many innovative and important advancements which would…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
We calculate the energy levels of a system of neutrinos undergoing collective oscillations as functions of an effective coupling strength and radial distance from the neutrino source using the quantum Lanczos (QLanczos) algorithm…
Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization. The quantum…
The Liouville-Lanczos approach to linear-response time-dependent density-functional theory is generalized so as to encompass electron energy-loss and inelastic X-ray scattering spectroscopies in periodic solids. The computation of virtual…
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…