Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors

Abstract

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction-vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that Krylov-space approach can be more accurate and efficient than conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.

8 pages, 7 figures

References in corpus (10)

• Real time evolution using the density matrix renormalization group
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Chebyshev matrix product state approach for spectral functions
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Spectral functions and time evolution from the Chebyshev recursion
• Density-matrix renormalisation group approach to quantum impurity problems
• High Energy Dynamics of the Single Impurity Anderson Model
• Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group
• Spectral Densities from Dynamic Density-Matrix Renormalization
• Density-matrix renormalization group methods for momentum- and frequency-resolved dynamical correlation functions

Cited by in corpus (9)

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• Block orbital-selective Mott insulators: a spin excitation analysis
• Magnetic excitation spectra of strongly correlated quasi-one dimensional systems: Heisenberg versus Hubbard-like behavior
• Prediction of exotic magnetic states in the alkali metal quasi-one-dimensional iron selenide compound Na${}_2$FeSe${}_2$
• Spectroscopic signatures of next-nearest-neighbor hopping in the charge and spin dynamics of doped one-dimensional antiferromagnets
• Signatures of pairing in the magnetic excitation spectrum of strongly correlated ladders
• Width of the charge-transfer peak in the SU(N) impurity Anderson model and its relevance to non-equilibrium transport
• Novel Block Excitonic Condensate at $n=3.5$ in a Spin-Orbit Coupled $t_{2g}$ Multiorbital Hubbard Model
• Dynamic structure factor from real time evolution and exact correction vectors with matrix product states