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Journal of Superconductivity and Novel Magnetism

Reducing Computational Time of Quantum Diagonalization Calculation for 2-Dimensional Strongly Correlated Systems

Sul-Ah Ahn, Myoung Won Cho

Published Jan 29, 2010• 0 citations
Publisher
DOI
10.1007/s10948-010-0725-9

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One of the most fascinating issues in modern condensed matter physics is to understand highly-correlated electronic structures and propose their novel device designs toward the reduced carbon-dioxide future. Among various developed numerical approaches for highly-correlated electrons, the density matrix renormalization group (DMRG) has been widely accepted as the most promising numerical scheme compared to Monte Carlo and exact diagonalization in terms of accuracy and accessible system size. In fact, DMRG almost perfectly resolves one-dimensional chain like long quantum systems. In this paper, we suggest its extended approach toward higher-dimensional systems by high-performanc computing techniques. The computing target in DMRG is a huge non-uniform sparse matrix diagonalization. In order to efficiently parallelize the part, we implement communication step doubling together with reuse of the mid-point data between the doubled two steps to avoid severe bottleneck of all-to-all communications essential for the diagonalization. The technique is successful even for clusters composed of more than 1000 cores and offers a trustworthy exploration way for two-dimensional highly-correlated systems.
We study photoinduced optical responses of one-dimensional strongly correlated electron systems. The optical conductivity spectra are calculated for the ground state and a photoexcited state in the one-dimensional Hubbard model at half filling by using the exact diagonalization method. It is found that, in the Mott insulator phase, the photoexcited state has large spectral weights including the Drude weight below the optical gap. As a consequence, the spectral weight above the optical gap is largely reduced. These results imply that a metallic state is induced by photoexcitation. Comparison between the photoexcited and hole-doped states shows that the photoexcitation is similar to chemical doping.