Package: pyblock3
pyblock3An Efficient python block-sparse tensor and MPS/DMRG LibraryCopyright (C) 2020-2021 The pyblock3 developers. All Rights Reserved.Authors:Huanchen Zhai@hczhai: MPS/MPO/DMRGYang Gao@yangcal: General fermionic tensorGarnet Kin-Lic Chan@gkc1000: Library designPlease 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/latestTutorial:https://colab.research.google.com/drive/1grQyYP9oTivjqQRZiwU40tF9SdWyrPfV?usp=sharingFeaturesBlock-sparse tensor algebra with quantum number symmetries:U(1) particle numberU(1) spinAbelian point group symmetryMPO constructionSVD approach for general fermionic HamiltonianConventional approach for quantum chemistry HamiltonianMPO/MPS algebraMPO compressionEfficient sweep algorithms for ab initio systems (2-site):Ground-state DMRG with perturbative noiseMPS compressionGreen's function (DDMRG++)Imaginary time evolution (time-step targeting approach)Real time evolution (time-step targeting approach)Finite-temperature DMRG (ancilla approach)InstallationUsingpip:pip install pyblock3To install the most recent development version, use:pip install pyblock3==<version> --extra-index-url=https://block-hczhai.github.io/pyblock3-preview/pypi/where<version>can be some development version number like0.2.7rc5.Or you can compile it manually:Dependence:python3,psutil,numba, andnumpy(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(orblas + lapack)WhenMKLis available, addcmakeoption:-DUSE_MKL=ON.Ifcmakecannot findMKL, one can add environment variable hintMKLROOT.C++ compiler:g++orclangicpccurrently not tested/supportedHigh 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 performanceWhenHPTTis available, addcmakeoption:-DUSE_HPTT=ON.Ifcmakecannot findHPTT, one can add environment variable hintHPTTHOME.openMP librarygomporiomp5(optional)This is required for multi-threading parallelization.For openMP disabled: addcmakeoption:-DOMP_LIB=SEQ.For gnu openMP (gomp): addcmakeoption:-DOMP_LIB=GNU.For intel openMP (iomp5): addcmakeoption:-DOMP_LIB=INTEL(default).Ifcmakecannot find openMP library, one can add the path tolibgomp.soorlibiomp5.soto environment variablePATH.To compile the C++ part of the code (for better performance):mkdir build
cd build
cmake .. -DUSE_MKL=ON -DUSE_HPTT=ON
makeAdd package root directory toPYTHONPATHbefore running the following examples.If you used directory names other thanbuildfor the build directory (which contains the compiled python extension),
you also need to add the build directory toPYTHONPATH.ExamplesGround-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 ClassWrite the C++ definition of the class (namedQPN, for example) insrc/qpn.hpp, which should be similar tosrc/sz.hpp.Add the following insrc/symmetry_tmpl.hppafteradd other symmetries hereline:#include "qpn.hpp"
 #define TMPL_Q QPN
 #include NAME_IMPL(TMPL_NAME,_tmpl.hpp)
 #undef TMPL_QNote that if multiple symmetry class are defined in the same filesrc/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 classSZand you want to save compiling time, the four lines forSZcan be removed/commented.Add the following insrc/main.hppafterbind extra symmetry hereline: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 classSZand you want to save compiling time, the two linesbind_ ...forSZcan be removed/commented.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