Direct Extension of Density-Matrix Renormalization Group to Two-Dimensional Quantum Lattice Systems: Studies of Parallel Algorithm, Accuracy, and Performance

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概要

• 論文の詳細を見る

• We parallelize the density-matrix renormalization group method to directly extend it to two-dimensional ($n$-leg) quantum lattice models. The parallelization is performed mainly on the diagonalization for the superblock Hamiltonian since this step requires enormous memory space as the leg number $n$ increases. The superblock Hamiltonian is divided into three parts, and the corresponding superblock vectors are transformed into matrices whose elements are uniformly distributed into processors. Parallel efficiency increases as the number of states kept, $m$, increases, and the obtained ground-state energy rapidly converges within a few sweeps. Furthermore, the present algorithm applied to doped 4-leg Hubbard ladders reaches their ground states, which satisfy the Lieb–Mattis theorem with $m$ much smaller than those used in different indirect algorithms.

• Physical Society of Japanの論文
• 2009-09-15

著者

• MACHIDA Masahiko

  Center for Promotion of Computational Science and Engineering,Japan Atomic Energy Research Institute

• Yamada Susumu

  Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Taito, Tokyo 110-0015

• Okumura Masahiko

  Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Taito, Tokyo 110-0015

• Machida Masahiko

  Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Taito, Tokyo 110-0015

関連論文

• Nonabelian Chiral Anomaly and the Spin Gap in One-Dimensional Interacting Electron Systems
• Direct Extension of Density-Matrix Renormalization Group to Two-Dimensional Quantum Lattice Systems: Studies of Parallel Algorithm, Accuracy, and Performance

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