The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs

Csaba Nemes, Gergely Barcza, Zoltán Nagy, Örs Legeza, Péter Szolgay

Research output: Contribution to journalArticle

6 Citations (Scopus)


In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.

Original languageEnglish
Pages (from-to)1570-1581
Number of pages12
JournalComputer Physics Communications
Issue number6
Publication statusPublished - Jun 2014



  • DMRG
  • FPGA acceleration
  • GPU acceleration
  • Strongly correlated systems

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)

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