Direct extension of the density-matrix renormalization group method toward two-dimensional large quantum lattices and related high-performance computing

DOI10.1007/s13160-011-0027-zzbMath1447.81083OpenAlexW1992437162MaRDI QIDQ692016

Susumu Yamada, Masahiko Okumura

Publication date: 4 December 2012

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-011-0027-z

zbMATH Keywords

eigenvalue problemsparallel and distributed computingmatrix-vector multiplicationDMRG method

Mathematics Subject Classification ID

Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) (68Q10) Quantum computation (81P68) Quantum field theory on lattices (81T25) Parallel numerical computation (65Y05) Renormalization group methods applied to problems in quantum field theory (81T17) Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Quantum measurement theory, state operations, state preparations (81P15)

Uses Software

• lobpcg.m

Cites Work

• Preconditioning eigensolvers -- an Oxymoron?
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• The density-matrix renormalization group
• Handbook of High-Temperature Superconductivity
• Lanczos Algorithms for Large Symmetric Eigenvalue Computations

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