SUNDMRG.jl

Traditional DMRG code with full SU(N) symmetry implementation
Author MGYamada
Github
Popularity
6 Stars
Updated Last
10 Months Ago
Started In
October 2023

SUNDMRG.jl

SUNDMRG.jl: traditional DMRG code with full SU(N) symmetry implementation. A part of the code is influenced by Simple DMRG. https://github.com/simple-dmrg/simple-dmrg

Features

  • Fully supporting 2D systems
  • Fully supporting MPI parallelization
  • Fully supporting CUDA and MAGMA
  • CUDA-aware MPI
  • File-IO

Installation

Before ]add, you must install MAGMA.jl@0.1.2-. https://github.com/MGYamada/MAGMA.jl After that, you can do:

]add https://github.com/MGYamada/SUNDMRG.jl.git

Usage

If you want to run the simulation of the SU(2) Heisenberg model on the 4x4 square lattice with a default setting, please use the following.

rank, dmrg = run_DMRG(SU(2)HeisenbergModel(), SquareLattice(4, 4), 100, [100, 200, 400, 800], 1600, CPUEngine)

dmrg is returned only when rank == 0 when you are using the MPI parallelization.

For a more detailed configuration, please look at the examples directory.

Please be careful that the expectation value of the bond operator is returned in the format of Pij - 1 / Nc for SU(Nc) for the accuracy.

SU(2)

SUNDMRG.jl supports an on-the-fly calculation of SU(2) symmetry coefficients (Wigner symbols). The bond Hamiltonian is Si・Sj in the SU(2) case, not Pij = 2 Si・Sj + 1 / 2. SiSj is also evaluated by Si・Sj, not Pij - 1 / 2.

Density matrix mixing

The density matrix mixing (sometimes called a noise term) is a technique to have a better convergence in DMRG. It perturbs the density matrix a little, avoiding being stuck in some local minima. The small perturbation is specified in the second term of the tuple for each sweep as follows.

rank, dmrg = run_DMRG(SU(3)HeisenbergModel(), SquareLattice(6, 6), (100, 1e-5), [(100, 1e-5), (200, 1e-6), (400, 1e-7), (800, 1e-8)], (1600, 0.0), CPUEngine; widthmax = widthmax, tables = tables)

The value has to become zero or a negligibly small value in the last few sweeps.

Dependency

  • Julia 1.6-
  • CUDA.jl 5.0.0-
  • MAGMA.jl 0.1.2-
  • SUNRepresentations.jl 0.1.2-
  • MPI.jl: We strongly recommend to use Open MPI.

TODO

  • Type piracy in lanczos.jl
  • Hybrid parallelization
  • Supporting the triangular lattice
  • Thick-restart Lanczos

Highly unlikely future features

  • Supporting the kagome lattice
  • MPS formulation
  • Supporting a spin system not with a fundamental representation per site

Open Question

Why do we need

signfactor = iseven(Nc) ? -1.0 : 1.0

in finite.jl?

License

MIT

Authors

  • Masahiko G. Yamada
  • James R. Garrison
  • Ryan V. Mishmash

Please inquire questions to Masahiko G. Yamada (@MGYamada). Some functions are written by @maartenvd. I would also thank Frank Pollmann and Karlo Penc for stimulating discussions.