ITensorMPS.jl

Finite MPS and MPO methods based on the Julia version of ITensor (ITensors.jl). See the ITensorMPS.jl documentation for more details.

Support

ITensorMPS.jl is supported by the Flatiron Institute, a division of the Simons Foundation.

All MPS/MPO code from ITensors.jl and ITensorTDVP.jl has been moved into this repository and this repository now relies on ITensors.jl v0.7 and above. All of the MPS/MPO functionality that was previously in ITensors.jl and ITensorTDVP.jl will be developed here from now on. For users of this repository, this change should not break any code, though please let us know if you have any issues.

Upgrade guide

If you are using any MPS/MPO functionality of ITensors.jl, such as the MPS and MPO types or constructors thereof (like random_mps), OpSum, siteinds, dmrg, apply, etc. you should install the ITensorMPS.jl package with import Pkg; Pkg.add("ITensorMPS") and add using ITensorMPS to your code. Additionally, if you are currently using ITensorTDVP.jl, you should replace using ITensorTDVP with using ITensorMPS in your code.

ITensorMPS.jl v0.2.1 release notes

New features

This release introduces a new (experimental) function expand for performing global Krylov expansion based on arXiv:2005.06104. It is a re-export of the expand function introduced in ITensorTDVP.jl v0.4.1, see the ITensorTDVP.jl v0.4.1 release notes for more details.

ITensorMPS.jl v0.2 release notes

Breaking changes

ITensorMPS.jl v0.2 has been released, which is a breaking release. It updates to using ITensorTDVP.jl v0.4, which has a number of breaking changes to the tdvp, linsolve, and dmrg_x functions. See the ITensorTDVP.jl v0.4 release notes for details.

Example DMRG Calculation

DMRG is an iterative algorithm for finding the dominant eigenvector of an exponentially large, Hermitian matrix. It originates in physics with the purpose of finding eigenvectors of Hamiltonian (energy) matrices which model the behavior of quantum systems.

using ITensors, ITensorMPS
let
  # Create 100 spin-one indices
  N = 100
  sites = siteinds("S=1", N)

  # Input operator terms which define
  # a Hamiltonian matrix, and convert
  # these terms to an MPO tensor network
  # (here we make the 1D Heisenberg model)
  os = OpSum()
  for j in 1:(N - 1)
    os += "Sz", j, "Sz", j + 1
    os += 0.5, "S+", j, "S-", j + 1
    os += 0.5, "S-", j, "S+", j + 1
  end
  H = MPO(os, sites)

  # Create an initial random matrix product state
  psi0 = random_mps(sites)

  # Plan to do 5 passes or 'sweeps' of DMRG,
  # setting maximum MPS internal dimensions
  # for each sweep and maximum truncation cutoff
  # used when adapting internal dimensions:
  nsweeps = 5
  maxdim = [10, 20, 100, 100, 200]
  cutoff = 1E-10

  # Run the DMRG algorithm, returning energy
  # (dominant eigenvalue) and optimized MPS
  energy, psi = dmrg(H, psi0; nsweeps, maxdim, cutoff)
  println("Final energy = $energy")

  nothing
end

# output

# After sweep 1 energy=-137.954199761732 maxlinkdim=9 maxerr=2.43E-16 time=9.356
# After sweep 2 energy=-138.935058943878 maxlinkdim=20 maxerr=4.97E-06 time=0.671
# After sweep 3 energy=-138.940080155429 maxlinkdim=92 maxerr=1.00E-10 time=4.522
# After sweep 4 energy=-138.940086009318 maxlinkdim=100 maxerr=1.05E-10 time=11.644
# After sweep 5 energy=-138.940086058840 maxlinkdim=96 maxerr=1.00E-10 time=12.771
# Final energy = -138.94008605883985

After sweep 1 energy=-137.49459254253506  maxlinkdim=9 maxerr=5.59E-16 time=17.470
After sweep 2 energy=-138.9351325614449  maxlinkdim=20 maxerr=5.10E-06 time=0.389
After sweep 3 energy=-138.94008111059603  maxlinkdim=91 maxerr=1.00E-10 time=3.426
After sweep 4 energy=-138.9400860547521  maxlinkdim=99 maxerr=1.19E-10 time=7.887
After sweep 5 energy=-138.94008607226354  maxlinkdim=95 maxerr=1.00E-10 time=8.374
Final energy = -138.94008607226354

You can find more examples of running dmrg and related algorithms here.

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