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Development of Numerical Algorithm for Quantum Atomic Gas

Research Project

Project/Area Number 18500033
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Software
Research InstitutionJapan Atomic Energy Agency

Principal Investigator

SUSUMU Yamada  Japan Atomic Energy Agency, Center for Computational Science & e-Systems, Scientist (80360436)

Co-Investigator(Kenkyū-buntansha) MACHIDA Masahiko  Japan Atomic Energy Agency, システム計算科学センター, Principal Researcher (60360434)
OHASHI Yoji  Keio University, Faculty of Science and Technology, Associate professor (60272134)
IMAMURA Toshiyuki  The University of Electro-Communications, Department of Computer Science, Associate professor (60361838)
松本 秀樹  筑波大学, 数理物質科学研究科, 教授 (40209648)
Project Period (FY) 2006 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,820,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2006: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsHigh Performance Comnuting / Density Matrix Renormalization Group / The Earth Simulator / Eigenvalue Solver / Parallel Comnuting / Fermion / Hubbard model
Research Abstract

In 2006, our research group developed a novel preconditioner for the conjugate gradient method in solving the ground state of the Hamiltonian matrix of the Hubbard model describing quantum atomic gases loaded on optical lattices. We proposed a preconditioner using an approximate eigenvalue obtained at each iteration step. The preconditioner improves the convergence property of the CG method by several times than that without the preconditioner. This research result was published in the transactions of the Japan Society for Computational Engineering and Science and selected as one of the outstanding paper award of JSCES.
In 2007, we focused on the Density Matrix Renormalization Group (DMRG) method, which is widely used by computational physicists as a high accuracy tool to obtain the ground state of large quantum lattice systems. It is well known that the DMRG method for 2-D models demands an enormous memory space. Therefore, we proposed a parallel algorithm of the DMRG, whose core is the parallelization of the matrix-vector multiplication repeated in solving the eigenvalue problem. Since the parallelization is made on the most time- and memory-consuming operation, the parallel DMRG method shows good parallel efficiency. We presented the results at the TASTED International Multi-Conference on Parallel and Distributed computing and Networks. Moreover, we examined 2-D Hubbard models systematically using our parallel DMRG method on SGI Altix 3700Bx2 in Japan Atomic Energy Agency, and published the physical insights obtained by this simulation in journals of physical field. (Phys. Rev. A)

Report

(3 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • Research Products

    (37 results)

All 2008 2007 2006

All Journal Article (28 results) (of which Peer Reviewed: 12 results) Presentation (9 results)

  • [Journal Article] Parallel Computing of Directly-extended Density-Matrix Renormalization Group to Two-dimensional Strongly Correlated Quantum Systems2008

    • Author(s)
      Susumu Yamada
    • Journal Title

      Proceedings of PDCN 2008

      Pages: 175-180

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Stripe formation in fermionic atoms on a two-dimensional optical lattice inside a box trap:Density-matrix renormalization-group studies for the repulsive Hubbard model with open boundary conditions2008

    • Author(s)
      Masahiko Machida
    • Journal Title

      Physical Review A 77

      Pages: 33619-33619

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Parallel Computing of Directly-extended Density-Matrix Renormalization Group to Two-dimensional Strongly Correlated Quantum Systems2008

    • Author(s)
      S. Yamada
    • Journal Title

      Proceedings of PDCN 2008

      Pages: 175-180

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Stripe formation in fermionic atoms on a two-dimensional optical lattice inside a box trap : Density-matrix renormalization-group studies for the repulsive Hubbard model with open boundary conditions2008

    • Author(s)
      M. Machida
    • Journal Title

      Physical Review A 77

      Pages: 33619-33619

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Parallel Computing of Directly-extended Density-Matrix Renormalization Group to Two-dimensional Strongly Correlated Quantum Systems2008

    • Author(s)
      Susumu Yamada
    • Journal Title

      Proceedings of PDCN2008

      Pages: 175-180

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stripe formation in fermionic atoms on a two-dimensional optical lattice inside a box trap:Density-matrix renormalization-group studies for therepulsive Hubbard model with open boundary conditions2008

    • Author(s)
      Masahiko Machida
    • Journal Title

      Physical Review A 77

      Pages: 33619-33619

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ultra Large-scale Exact-diagonalization for Confined Fermion-Hubbard Model on the Earth Simulator:Exploration of Superfluidity in Confined Strongly-Correlated Systems2007

    • Author(s)
      Susumu Yamada
    • Journal Title

      Journal of the Earth Simulator 7

      Pages: 23-35

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Strong pairing and microscopic inhomogeneity of lattice fermion systems2007

    • Author(s)
      Susumu Yamada
    • Journal Title

      Physica C 463-465

      Pages: 103-106

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Ultra Large-scale Exact-diagonalization for Confined Fermion-Hubbard Model on the Earth Simulatior : Exploration of Superfluidity in Confined Strongly-Correlated Systems2007

    • Author(s)
      S. Yamada
    • Journal Title

      Journal of the Earth Simulator 7

      Pages: 23-35

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Strong pairing and microscopic inhomogeneity of lattice fermion systems2007

    • Author(s)
      S. Yamada
    • Journal Title

      Physica C 463-465

      Pages: 103-106

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 量子大規模固有値問題における共役勾配法の収束性:適応的シフト前処理の収束性の評価2006

    • Author(s)
      山田進
    • Journal Title

      日本計算工学会論文集 Vol.2006

      Pages: 20060027-20060027

    • NAID

      130008056184

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Novel pairing in the Hubbard model with confinement potential2006

    • Author(s)
      M.Machida
    • Journal Title

      Physica C 445-448

      Pages: 90-93

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On-site pairing and microscopic inhomogeneneity in confined lattice fermion systems2006

    • Author(s)
      M.Machida
    • Journal Title

      Phys.Rev.A 74

      Pages: 53621-53621

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Time-dependent Ginzburg-Landau Theory for Atomic Fermi Gases near BCS-BEC Crossover2006

    • Author(s)
      M.Machida
    • Journal Title

      Phys.Rev.A 74

      Pages: 33603-33603

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Microscopic Structure of a Quantized Vortex Core in Atomic Fermi Gases2006

    • Author(s)
      M.Machida
    • Journal Title

      Phys.Rev.A 74

      Pages: 23621-23621

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Effects of Edge Boundaries on Josephson Vortices in Finite-Size Layered High-Tc Superconductors2006

    • Author(s)
      M.Machida
    • Journal Title

      Phys.Rev.Lett. 96

      Pages: 97002-97002

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Preconditioned Conjugate Gradient Method for Large-Scale Eigenvalue Problem of Quantum Problem : Convergence Property of Adaptive-shift Preconditioner(in Japanese)2006

    • Author(s)
      A. Yamada
    • Journal Title

      Transactions of JSCES, Egret Himeji(Himeji)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Novel pairing in the Hubbard model with confinement potential2006

    • Author(s)
      M. Machida
    • Journal Title

      Physica C, Egret Himeji(Himeji)

      Pages: 90-93

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On-site pairing and microscopic inhomogeneneity in confined lattice fermion systems2006

    • Author(s)
      M. Machida
    • Journal Title

      Phys. Rev. A, Tampa(USA)

      Pages: 53621-53621

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Time-dependent Ginzburg-Landau Theory for Atomic Fermi Gases near BCS-BEC Crossover2006

    • Author(s)
      M. Machida
    • Journal Title

      Phys. Rev. A, Tohoku University, Sendai(Japan)

      Pages: 33603-33603

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Microscopic Structure of a Quantized Vortex Core in Atomic Fermi Gases2006

    • Author(s)
      M. Machida
    • Journal Title

      Phys. Rev. A, kyoto(Japan)

      Pages: 23621-23621

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Effects of Edge Boundaries on Josephson Vortices in Finite-Size Layered High-Tc Superconductors2006

    • Author(s)
      M. machida
    • Journal Title

      Phys. Rev. Lett., Innsbruck(Austria)

      Pages: 97002-97002

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 量子大規模固有値問題における共役勾配法の収束性 : 適応的シフト前処理の収束性の評価2006

    • Author(s)
      山田進, 今村俊幸, 町田昌彦
    • Journal Title

      日本計算工学会論文集 Vol.2006

      Pages: 20060027-20060027

    • NAID

      130008056184

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Novel pairing in the Hubbard model with confinement potential2006

    • Author(s)
      M.Machida, S.Yamada, Y.Ohashi, H.Matsumoto
    • Journal Title

      Physica C Vol.445-448

      Pages: 90-93

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On-site pairing and microscopic inhomogenenetity in confined lattice fermion systems2006

    • Author(s)
      M.Machida, S.Yamada, Y.Ohashi, H.Matsumoto
    • Journal Title

      Phys.Rev.A 74

      Pages: 53621-53621

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Time-dependent Ginzburg-Landau Theory for Atomic Fermi Gases near BCS-BEC Crossover2006

    • Author(s)
      M.Machida, T.Koyama
    • Journal Title

      Phys. Rev. A 74

      Pages: 33603-33603

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Microscopic Structure of a Quantized Vortex Core in Atomic Fermi Gases2006

    • Author(s)
      M.Machida, Y.Ohashi, T.Koyama
    • Journal Title

      Phys. Rev. A 74

      Pages: 23621-23621

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Effects of Edge Boundaries on Josephson Vortices in Finite-Size Layered High-Tc Superconductors2006

    • Author(s)
      M.Machida
    • Journal Title

      Phys. Rev. Lett. 96

      Pages: 97002-97002

    • Related Report
      2006 Annual Research Report
  • [Presentation] 超大規模量子計算が拓く強相関フェルミ原子ガスの新たな世界2008

    • Author(s)
      町田昌彦
    • Organizer
      HPCS2008
    • Place of Presentation
      Tokyo,Japan
    • Year and Date
      2008-01-18
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Parallel Computing of Directly-extended Density-Matrix Renormalization Group to Two-dimensional Strongly Correlated Quantum Systems2008

    • Author(s)
      Susumu Yamada
    • Organizer
      The 23rd IASTED International Multi-Conference on Parallel and Distributed computing and Networks
    • Place of Presentation
      Innsbruck Austria
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Parallel Computing of Directly-extended Density-Matrix Renormalization Group to Two-dimensional Strongly Correlated Quantum Systems2008

    • Author(s)
      Susumu Yamada
    • Organizer
      The 23rdLASTED International Multi-Conference on Parallel and Distributed computing and Networks
    • Place of Presentation
      Innsbruck(Austria)
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] High Performance Computing for Eigenvalue Solver to Coupled Josephson Junctions on the Earth Simulator2007

    • Author(s)
      Susumu Yamada
    • Organizer
      APCOM'07
    • Place of Presentation
      Kyoto(Japan)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Tera-flops Quantum Simulation for Superconducting Nano-device:High-Performance Eigenvalue Solver on the Earth Simulator2007

    • Author(s)
      Susumu Yamada
    • Organizer
      7-th Teraflop Workshop
    • Place of Presentation
      Tohoku University,Sendai,Japan
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Tera-flops Quantum Simulation for Superconduction Nano-device : High-Performance Eigenvalue Solver on the Earth Simulator2007

    • Author(s)
      Susumu Yamada
    • Organizer
      7-th Teraflop Workshop
    • Place of Presentation
      Tohoku University, Sendai(Japan)
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] High Performance Computing for Eigenvalue Solver to Coupled Josephson Junctions on the Earth Simulator2007

    • Author(s)
      Susumu Yamada
    • Organizer
      APCOM'07
    • Place of Presentation
      kyoto(Japan)
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] High-Performance Computing for Exact Numerical Approaches to Quantum Many-Body Problems on the Earth Simulator,2006

    • Author(s)
      M.Machida
    • Organizer
      Supercomputing 2006
    • Place of Presentation
      Tampa(USA)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] High-Performance Computing for Exact Numerical Approaches to Quantum many-Body Problems on the Earth Simulator2006

    • Author(s)
      M. Machida
    • Organizer
      Supercomputing 2006
    • Place of Presentation
      Tampa(USA)
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2006-04-01   Modified: 2016-04-21  

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