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Title: Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate 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. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Authors:
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 94; Journal Issue: 5; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Research Org:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE
OSTI Identifier:
1361304
Alternate Identifier(s):
OSTI ID: 1333029

None, None. Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors. United States: N. p., Web. doi:10.1103/PhysRevE.94.053308.
None, None. Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors. United States. doi:10.1103/PhysRevE.94.053308.
None, None. 2016. "Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors". United States. doi:10.1103/PhysRevE.94.053308. https://www.osti.gov/servlets/purl/1361304.
@article{osti_1361304,
title = {Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors},
author = {None, None},
abstractNote = {Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate 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. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.},
doi = {10.1103/PhysRevE.94.053308},
journal = {Physical Review E},
number = 5,
volume = 94,
place = {United States},
year = {2016},
month = {11}
}