Related papers: Prony methods for extracting excited states
The Logarithmic Linear Relaxation (LLR) algorithm is an efficient method for computing densities of states for systems with a continuous spectrum. A key feature of this method is exponential error reduction, which allows us to evaluate the…
In this communication, we propose a method for obtaining isolated excited states within the Full Configuration Interaction Quantum Monte Carlo framework. This method allows for stable sampling with respect to collapse to lower energy states…
Systems of Prony type appear in various signal reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. We propose a novel approach for solving Prony-type systems, which…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
In the construction of diabatic vibronic Hamiltonians for quantum dynamics in the excited-state manifold of molecules, the coupling constants are often extracted solely from information on the excited-state energies. Here, a new protocol is…
Excited states are extracted from lattice correlation functions using a non-uniform prior on the model parameters. Models for both a single exponential and a sum of exponentials are considered, as well as an alternate model for the…
The convergent iterative procedure for solving the groundstate Schroedinger equation is extended to derive the excitation energy and the wave function of the low-lying excited states. The method is applied to the one-dimensional quartic…
Prony's method, in its various concrete algorithmic realizations, is concerned with the reconstruction of a sparse exponential sum from integer samples. In several variables, the reconstruction is based on finding the variety for a zero…
Among lattice configurations of densely packed hard ellipses, Monte Carlo simulations are used to identify the so-called parallel and diagonal lattices as the two favourable states. The free energies of these two states are computed for…
Using a new quark-field construction algorithm and a large variational basis of operators, we extract a highly excited isovector meson spectrum on dynamical anisotropic lattices. We show how carefully constructed operators can be used to…
We present the ground and excited state spectra of singly, doubly and triply charmed baryons by using dynamical lattice QCD. A large set of baryonic operators that respect the symmetries of the lattice and are obtained after subduction from…
The problem of having to reconstruct the decay rates and corresponding amplitudes of the single-exponential components of a noisy multi-exponential signal is common in many other areas of physics and engineering besides lattice field…
Let $B$ be an unknown linear evolution process on $\mathbb C^d\simeq l^2(\mathbb Z_d)$ driving an unknown initial state $x$ and producing the states $\{B^\ell x, \ell = 0,1,\ldots\}$ at different time levels. The problem under consideration…
We solve a model of interacting electrons coupled to longitudinal phonons using the density matrix renormalisation group method. The model is parametrised for polyenes. We calculate the ground state, and first excited odd-parity singlet and…
We use the phenomenon of electromagnetically-induced transparency in a three-level atomic system for hyperfine spectroscopy of upper states that are not directly coupled to the ground state. The three levels form a ladder system: the probe…
We show that Prony's method provides the full solution to the nonlinear equations of the connected--moments expansion (CMX). Knowledge of all the parameters in the CMX ansatz is useful for the analysis of the convergence properties of the…
In this paper, we develop a general method to estimate the instantaneous frequencies of the modes making up a multicomponent signal when the former exhibit interference in the time-frequency plane. In particular, studying the representation…
We analyze the systematic errors made when using the generalized eigenvalue problem to extract energies and matrix elements in lattice gauge theory. Effective theories such as HQET are also discussed. Numerical results are shown for the…
Progress in calculating the spectrum of excited baryons and mesons in lattice QCD is described. Correlation matrices of sets of spatially-extended hadron operators have been studied and their effectiveness in facilitating the extraction of…
In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a N\'eel model state with spins aligned in the $z$-direction, for both the ground- and excited-state properties of the spin-half {\it…