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 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. Further, 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:
-
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)
- Publication Date:
- 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). Scientific User Facilities Division
- OSTI Identifier:
- 1361304
- Alternate Identifier(s):
- OSTI ID: 1333029
- Grant/Contract Number:
- AC05-00OR22725
- Resource 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)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE
Citation Formats
Nocera, A., and Alvarez, G. Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors. United States: N. p., 2016.
Web. doi:10.1103/physreve.94.053308.
Nocera, A., & Alvarez, G. Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors. United States. https://doi.org/10.1103/physreve.94.053308
Nocera, A., and Alvarez, G. Mon .
"Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors". United States. https://doi.org/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 = {Nocera, A. and Alvarez, G.},
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. Further, 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 = {Mon Nov 21 00:00:00 EST 2016},
month = {Mon Nov 21 00:00:00 EST 2016}
}
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