pyblock3

An Efficient python block-sparse tensor and MPS/DMRG Library

Copyright (C) 2020-2021 The pyblock3 developers. All Rights Reserved.

Authors:

• Huanchen Zhai @hczhai: MPS/MPO/DMRG
• Yang Gao @yangcal: General fermionic tensor
• Garnet Kin-Lic Chan @gkc1000: Library design

Please cite this work as:

Huanchen Zhai, Yang Gao, and Garnet K.-L. Chan. pyblock3: an efficient python block-sparse tensor and MPS/DMRG library. 2021; https://github.com/block-hczhai/pyblock3-preview.

Documentation: https://pyblock3.readthedocs.io/en/latest

Tutorial: https://colab.research.google.com/drive/1grQyYP9oTivjqQRZiwU40tF9SdWyrPfV?usp=sharing

Features

• Block-sparse tensor algebra with quantum number symmetries:
  • U(1) particle number
  • U(1) spin
  • Abelian point group symmetry
• MPO construction
  • SVD approach for general fermionic Hamiltonian
  • Conventional approach for quantum chemistry Hamiltonian
• MPO/MPS algebra
  • MPO compression
• Efficient sweep algorithms for ab initio systems (2-site):
  • Ground-state DMRG with perturbative noise
  • MPS compression
  • Green's function (DDMRG++)
  • Imaginary time evolution (time-step targeting approach)
  • Real time evolution (time-step targeting approach)
  • Finite-temperature DMRG (ancilla approach)

Installation

Dependence: python3, psutil, numba, and numpy (version >= 1.17.0). pyblock3 can run in pure python mode, in which no C++ source code is required to be compiled.

For optimal performance, the C++ source code is used and there are some additional dependences:

• pybind11 (https://github.com/pybind/pybind11)
• cmake (version >= 3.0)
• MKL (or blas + lapack)
  • When MKL is available, add cmake option: -DUSE_MKL=ON.
  • If cmake cannot find MKL, one can add environment variable hint MKLROOT.
• C++ compiler: g++ or clang
  • icpc currently not tested/supported
• High performance Tensor Transposition library: hptt (https://github.com/springer13/hptt) (optional)
  • For CPU with AVX512 flag, one can use this AVX512 version (https://github.com/hczhai/hptt)
  • HPTT is important for optimal performance
  • When HPTT is available, add cmake option: -DUSE_HPTT=ON.
  • If cmake cannot find HPTT, one can add environment variable hint HPTTHOME.
• openMP library gomp or iomp5 (optional)
  • This is required for multi-threading parallelization.
  • For openMP disabled: add cmake option: -DOMP_LIB=SEQ.
  • For gnu openMP (gomp): add cmake option: -DOMP_LIB=GNU.
  • For intel openMP (iomp5): add cmake option: -DOMP_LIB=INTEL (default).
  • If cmake cannot find openMP library, one can add the path to libgomp.so or libiomp5.so to environment variable PATH.

To compile the C++ part of the code (for better performance):

mkdir build
cd build
cmake .. -DUSE_MKL=ON -DUSE_HPTT=ON
make

Examples

Add package root directory to PYTHONPATH before running the following examples.

If you used directory names other than build for the build directory (which contains the compiled python extension), you also need to add the build directory to PYTHONPATH.

Ground-state DMRG (H8 STO6G) in pure python (52 seconds):

import numpy as np
from pyblock3.algebra.mpe import MPE
from pyblock3.hamiltonian import Hamiltonian
from pyblock3.fcidump import FCIDUMP

fd = 'data/H8.STO6G.R1.8.FCIDUMP'
bond_dim = 250
hamil = Hamiltonian(FCIDUMP(pg='d2h').read(fd), flat=False)
mpo = hamil.build_qc_mpo()
mpo, _ = mpo.compress(cutoff=1E-9, norm_cutoff=1E-9)
mps = hamil.build_mps(bond_dim)

dmrg = MPE(mps, mpo, mps).dmrg(bdims=[bond_dim], noises=[1E-6, 0],
    dav_thrds=[1E-3], iprint=2, n_sweeps=10)
ener = dmrg.energies[-1]
print("Energy = %20.12f" % ener)

Ground-state DMRG (H8 STO6G) with C++ optimized core functions (0.87 seconds):

import numpy as np
from pyblock3.algebra.mpe import MPE
from pyblock3.hamiltonian import Hamiltonian
from pyblock3.fcidump import FCIDUMP

fd = 'data/H8.STO6G.R1.8.FCIDUMP'
bond_dim = 250
hamil = Hamiltonian(FCIDUMP(pg='d2h').read(fd), flat=True)
mpo = hamil.build_qc_mpo()
mpo, _ = mpo.compress(cutoff=1E-9, norm_cutoff=1E-9)
mps = hamil.build_mps(bond_dim)

dmrg = MPE(mps, mpo, mps).dmrg(bdims=[bond_dim], noises=[1E-6, 0],
    dav_thrds=[1E-3], iprint=2, n_sweeps=10)
ener = dmrg.energies[-1]
print("Energy = %20.12f" % ener)

The printed ground-state energy for this system should be -4.345079402665.

Adding Extra Symmetry Class

1. Write the C++ definition of the class (named QPN, for example) in src/qpn.hpp, which should be similar to src/sz.hpp.

2. Add the following in src/symmetry_tmpl.hpp after add other symmetries here line:

    #include "qpn.hpp"
    #define TMPL_Q QPN
    #include NAME_IMPL(TMPL_NAME,_tmpl.hpp)
    #undef TMPL_Q
   

   Note that if multiple symmetry class are defined in the same file src/qpn.hpp, you may only write #include "qpn.hpp" once. The other three lines have to be repeated for each symmetry class. If you do not need the default symmetry class SZ and you want to save compiling time, the four lines for SZ can be removed/commented.

3. Add the following in src/main.hpp after bind extra symmetry here line:

    py::module m_qpn = m.def_submodule("qpn", "General other symmetry.");
    bind_sparse_tensor<QPN>(m_qpn, m, "QPN");
   

   If you do not need the default symmetry class SZ and you want to save compiling time, the two lines bind_ ... for SZ can be removed/commented.

4. In python script, use the following to indicate which symmetry class is being used:

    if DEFAULT_SYMMETRY == SZ:
        import block3.sz as block3
    elif DEFAULT_SYMMETRY == QPN:
        import block3.qpn as block3