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Error Analysis of the Density-Matrix Renormalization Group Algorithm for a Chain of Harmonic Oscillators |
| MA Yong-Jun1, WANG Jia-Xiang1**, XU Xin-Ye1, WEI Qi1, Sabre Kais2,3 |
1State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062
2Departments of Chemistry and Physics, Purdue University, Indiana 47907, USA
3Qatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar
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| Cite this article: |
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MA Yong-Jun, WANG Jia-Xiang, XU Xin-Ye et al 2014 Chin. Phys. Lett. 31 060501 |
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Abstract We investigate the application of the density-matrix renormalization group (DMRG) algorithm to a one-dimensional harmonic oscillator chain and compare the results with exact solutions, aiming at improving the algorithm's efficiency. It is demonstrated that the algorithm can show quite accurate results if the procedure is properly organized; for example, by using the optimized bases. The errors of calculated ground state energy and the energy gap between the ground state and the first excited state are analyzed, and they are found to be critically dependent upon the size of the system or the energy level structure of the studied system and the number of states targeted during the DMRG procedure.
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Published: 26 May 2014
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| PACS: |
05.10.Cc
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(Renormalization group methods)
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63.20.D-
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(Phonon states and bands, normal modes, and phonon dispersion)
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Abstract
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