block2 0.4.1

An efficient MPO implementation of DMRG for quantum chemistry.

block2

The block2 code provides an efficient highly scalable implementation of the Density Matrix Renormalization Group (DMRG) for quantum chemistry, based on Matrix Product Operator (MPO) formalism.

The block2 code is developed as an improved version of StackBlock, where the low-level structure of the code has been completely rewritten. The block2 code is developed and maintained in Garnet Chan group at Caltech.

Main contributors:

• Huanchen Zhai @hczhai: DMRG and parallelization
• Henrik R. Larsson @h-larsson: DMRG-MRCI/MRPT, large site, Green's function in frequency and time for finite temp.
• Seunghoon Lee @seunghoonlee89: Stochastic perturbative DMRG
• Zhi-Hao Cui @zhcui: User interface

If you find this package useful for your scientific research, please cite the work as:

Zhai, H., Chan, G. K. Low communication high performance ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics 2021, 154, 224116.

One can install block2 using pip:

• OpenMP-only version (no MPI dependence)

  pip install block2
  

• Hybrid openMP/MPI version (requiring openMPI 4.0.x installed)

  pip install block2-mpi
  

• Binary format are prepared via pip for python 3.7, 3.8, and 3.9 with macOS (no-MPI) or Linux (no-MPI/openMPI). If these binaries have some problems, you can use the --no-binary option of pip to force building from source.

To run a DMRG calculation, please use the following command:

block2main dmrg.conf > dmrg.out

where dmrg.conf is the StackBlock style input file and dmrg.out contains the outputs.

Documentation: https://block2.readthedocs.io/en/latest/

Source code: https://github.com/block-hczhai/block2-preview

Features

• State symmetry
  • U(1) particle number symmetry
  • SU(2) or U(1) spin symmetry
  • Abelian point group symmetry
  • Translational / Lz symmetry
• Sweep algorithms (1-site / 2-site / 2-site to 1-site transition)
  • Ground-State DMRG
    • Decomposition types: density matrix / SVD
    • Noise types: wavefunction / density matrix / perturbative
  • Multi-Target Excited-State DMRG
    • State-averaged / state-specific
  • MPS compression / addition
  • Expectation
  • Imaginary / real time evolution
    • Hermitian / non-Hermitian Hamiltonian
    • Time-step targeting method
    • Time dependent variational principle method
  • Green's function
• Finite-Temperature DMRG (ancilla approach)
  • Green's function
  • Time evolution
• Low-Temperature DMRG (partition function approach)
• Particle Density Matrix (1-site / 2-site)
  • 1PDM / 2PDM
  • Transition 1PDM
  • Spin / charge correlation
• Quantum Chemistry MPO
  • Normal-Complementary (NC) partition
  • Complementary-Normal (CN) partition
  • Conventional scheme (switch between NC and CN near the middle site)
• Symbolic MPO simplification
• MPS initialization using occupation number
• Supported matrix representation of site operators
  • Block-sparse (outer) / dense (inner)
  • Block-sparse (outer) / elementwise-sparse (CSR, inner)
• Fermionic MPS algebra (non-spin-adapted only)
• Determinant/CSF overlap sampling
• Multi-level parallel DMRG
  • Parallelism over sites (2-site only)
  • Parallelism over sum of MPOs (non-spin-adapted only)
  • Parallelism over operators (distributed/shared memory)
  • Parallelism over symmetry sectors (shared memory)
  • Parallelism within dense matrix multiplications (MKL)
• Stochastic perturbative DMRG
• Uncontracted dynamic correlation
  • DMRG Multi-Reference Configuration Interaction (MRCI) of arbitrary order
  • DMRG Multi-Reference Averaged Quadratic Coupled Cluster (AQCC)/ Coupled Pair Functional (ACPF)
  • DMRG NEVPT2/3/..., REPT2/3/..., MR-LCC, ...
• Orbital Reordering
  • Fiedler
  • Genetic algorithm
• MPS Transformation
  • SU2 to SZ mapping
  • Point group mapping
  • Orbital basis rotation

References

Quantum Chemisty DMRG

• Chan, G. K.-L.; Head-Gordon, M. Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group. The Journal of Chemical Physics 2002, 116, 4462–4476. https://doi.org/10.1063/1.1449459.
• Sharma, S.; Chan, G. K.-L. Spin-adapted density matrix renormalization group algorithms for quantum chemistry. The Journalof Chemical Physics 2012, 136, 124121. https://doi.org/10.1063/1.3695642.
• Wouters, S.; Van Neck, D. The density matrix renormalization group for ab initio quantum chemistry. The European Physical Journal D 2014, 68, 272. https://doi.org/10.1140/epjd/e2014-50500-1.

Parallelization

• Chan, G. K.-L. An algorithm for large scale density matrix renormalization group calculations. The Journal of Chemical Physics 2004, 120, 3172–3178. https://doi.org/10.1063/1.1638734.
• Chan, G. K.-L.; Keselman, A.; Nakatani, N.; Li, Z.; White, S. R. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics 2016, 145, 014102. https://doi.org/10.1063/1.4955108.
• Stoudenmire, E.; White, S. R. Real-space parallel density matrix renormalization group. Physical Review B 2013, 87, 155137. https://doi.org/10.1103/PhysRevB.87.155137.
• Zhai, H., Chan, G. K. Low communication high performance ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics 2021, 154, 224116. https://doi.org/10.1063/5.0050902.

Spin-Orbit Coupling

• Sayfutyarova, E. R., Chan, G. K. L. A state interaction spin-orbit coupling density matrix renormalization group method. The Journal of Chemical Physics 2016, 144, 234301. https://doi.org/10.1063/1.4953445.
• Sayfutyarova, E. R., Chan, G. K. L. Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group. The Journal of Chemical Physics 2018, 148, 184103. https://doi.org/10.1063/1.5020079.

Green's Function

• Ronca, E., Li, Z., Jimenez-Hoyos, C. A., Chan, G. K. L. Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians. Journal of Chemical Theory and Computation 2017, 13, 5560-5571. https://doi.org/10.1021/acs.jctc.7b00682.

Finite-Temperature DMRG

• Feiguin, A. E., White, S. R. Finite-temperature density matrix renormalization using an enlarged Hilbert space. Physical Review B 2005, 72, 220401. https://doi.org/10.1103/PhysRevB.72.220401.
• Feiguin, A. E., White, S. R. Time-step targeting methods for real-time dynamics using the density matrix renormalization group. Physical Review B 2005, 72, 020404. https://doi.org/10.1103/PhysRevB.72.020404.

Linear Response

• Sharma, S., Chan, G. K. Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states. Journal of Chemical Physics 2014, 141, 111101. https://doi.org/10.1063/1.4895977.

Perturbative Noise

• White, S. R. Density matrix renormalization group algorithms with a single center site. Physical Review B 2005, 72, 180403. https://doi.org/10.1103/PhysRevB.72.180403.
• Hubig, C., McCulloch, I. P., Schollwöck, U., Wolf, F. A. Strictly single-site DMRG algorithm with subspace expansion. Physical Review B 2015, 91, 155115. https://doi.org/10.1103/PhysRevB.91.155115.

Particle Density Matrix

• Ghosh, D., Hachmann, J., Yanai, T., Chan, G. K. L. Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene. The Journal of Chemical Physics 2008, 128, 144117. https://doi.org/10.1063/1.2883976.

Multi-Reference Correlation Theories

• Szalay, P. G.; Müller, T.; Gidofalvi, G.; Lischka, H.; Shepard, R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chemical Reviews 2012, 112, 108-181. https://doi.org/10.1021/cr200137a.

• Gdanitz, R. J., Ahlrichs, R. The Averaged Coupled-Pair Functional (ACPF): A Size-Extensive Modification of MR CI(SD). Chemical Physics Letters 1988, 143, 413-420. https://doi.org/10.1016/0009-2614(88)87388-3.

• Szalay, P. G., Bartlett, R. J. Multi-Reference Averaged Quadratic Coupled-Cluster Method: A Size-Extensive Modification of Multi-Reference CI. Chemical Physics Letters 1993, 214, 481-488. https://doi.org/10.1016/0009-2614(93)85670-J.

• Laidig, W. D.; Bartlett, R. J. A Multi-Reference Coupled-Cluster Method for Molecular Applications. Chemical Physics Letters 1984, 104, 424-430. https://doi.org/10.1016/0009-2614(84)85617-1.

• Laidig, W. D., Saxe, P., Bartlett, R. J. The Description of N 2 and F 2 Potential Energy Surfaces Using Multireference Coupled Cluster Theory. The Journal of Chemical Physics 1987, 86, 887-907. https://doi.org/10.1063/1.452291.

• Angeli, C., Cimiraglia, R., Evangelisti, S., Leininger, T., Malrieu, J.-P. Introduction of N-Electron Valence States for Multireference Perturbation Theory. J. Chem. Phys. 2001, 114, 10252–10264. https://doi.org/10.1063/1.1361246.

• Angeli, C., Pastore, M., Cimiraglia, R. New Perspectives in Multireference Perturbation Theory: The n-Electron Valence State Approach. Theor Chem Account 2007, 117, 743–754. https://doi.org/10.1007/s00214-006-0207-0.

• Fink, R. F. The Multi-Reference Retaining the Excitation Degree Perturbation Theory: A Size-Consistent, Unitary Invariant, and Rapidly Convergent Wavefunction Based Ab Initio Approach. Chemical Physics 2009, 356, 39-46. https://doi.org/10.1016/j.chemphys.2008.10.004.

• Fink, R. F. Two New Unitary-Invariant and Size-Consistent Perturbation Theoretical Approaches to the Electron Correlation Energy. Chemical Physics Letters 2006, 428, 461–466. https://doi.org/10.1016/j.cplett.2006.07.081.

• Sharma, S., Chan, G. K.-L. Communication: A Flexible Multi-Reference Perturbation Theory by Minimizing the Hylleraas Functional with Matrix Product States. The Journal of Chemical Physics 2014, 141, 111101. https://doi.org/10.1063/1.4895977.

• Sharma, S., Alavi, A. Multireference Linearized Coupled Cluster Theory for Strongly Correlated Systems Using Matrix Product States. The Journal of Chemical Physics 2015, 143, 102815. https://doi.org/10.1063/1.4928643.

• Sharma, S., Jeanmairet, G., Alavi, A. Quasi-Degenerate Perturbation Theory Using Matrix Product States. The Journal of Chemical Physics 2016, 144, 034103. https://doi.org/10.1063/1.4939752.

Determinant Coefficients

• Lee, S., Zhai, H., Sharma, S., Umrigar, C. J., Chan, G. K. L. Externally Corrected CCSD with Renormalized Perturbative Triples (R-ecCCSD (T)) and the Density Matrix Renormalization Group and Selected Configuration Interaction External Sources. Journal of Chemical Theory and Computation 2021, 17, 3414-3425. https://doi.org/10.1021/acs.jctc.1c00205.

Perturbative DMRG

• Guo, S., Li, Z., Chan, G. K. L. Communication: An efficient stochastic algorithm for the perturbative density matrix renormalization group in large active spaces. The Journal of chemical physics 2018, 148, 221104. https://doi.org/10.1063/1.5031140.
• Guo, S., Li, Z., Chan, G. K. L. A perturbative density matrix renormalization group algorithm for large active spaces. Journal of chemical theory and computation 2018, 14, 4063-4071. https://doi.org/10.1021/acs.jctc.8b00273.

Orbital Reordering

• Olivares-Amaya, R.; Hu, W.; Nakatani, N.; Sharma, S.; Yang, J.;Chan, G. K.-L. The ab-initio density matrix renormalization group in practice. The Journal of Chemical Physics 2015, 142, 034102. https://doi.org/10.1063/1.4905329.

Manual Installation

Dependence: pybind11, python3, and mkl (or blas + lapack).

For distributed parallel calculation, mpi library is required.

For unit tests, googletest is required.

cmake (version >= 3.0) can be used to compile C++ part of the code, as follows:

mkdir build
cd build
cmake .. -DUSE_MKL=ON -DBUILD_LIB=ON -DLARGE_BOND=ON
make -j 10

This will build the python extension (using 10 CPU cores) (serial code).

MKL

If -DUSE_MKL=ON is not given, blas and lapack are required (with limited support for multi-threading).

Use -DUSE_MKL64=ON instead of -DUSE_MKL=ON to enable using matrices with 64-bit integer type.

Serial compilation

By default, the C++ templates will be explicitly instantiated in different compilation units, so that parallel compilation is possible.

Alternatively, one can do single-file compilation using -DEXP_TMPL=NONE, then total compilation time can be saved by avoiding unnecessary template instantiation, as follows:

cmake .. -DUSE_MKL=ON -DBUILD_LIB=ON -DEXP_TMPL=NONE
make -j 1

This may take 11 minutes, requiring 14 GB memory.

MPI version

Adding option -DMPI=ON will build MPI parallel version. The C++ compiler and MPI library must be matched. If necessary, environment variables CC, CXX, and MPIHOME can be used to explicitly set the path.

For mixed openMP/MPI, use mpirun --bind-to none -n ... or mpirun --bind-to core --map-by ppr:$NPROC:node:pe=$NOMPT ... to execute binary.

Binary build

To build unit tests and binary executable (instead of python extension), use the following:

cmake .. -DUSE_MKL=ON -DBUILD_TEST=ON

TBB (Intel Threading Building Blocks)

Adding (optional) option -DTBB=ON will utilize malloc from tbbmalloc. This can improve multi-threading performance.

openMP

If gnu openMP library libgomp is not available, one can use intel openMP library.

The following will switch to intel openMP library (incompatible with -fopenmp):

cmake .. -DUSE_MKL=ON -DBUILD_LIB=ON -DOMP_LIB=INTEL

The following will use sequential mkl library:

cmake .. -DUSE_MKL=ON -DBUILD_LIB=ON -DOMP_LIB=SEQ

The following will use tbb mkl library:

cmake .. -DUSE_MKL=ON -DBUILD_LIB=ON -DOMP_LIB=TBB -DTBB=ON

Note: for CSR sparse MKL + ThreadingTypes::Operator, if -DOMP_LIB=GNU, it is not possible to set both n_threads_mkl not equal to 1 and n_threads_op not equal to 1. In other words, nested openMP is not possible for CSR sparse matrix (generating wrong result/non-convergence). For -DOMP_LIB=SEQ, CSR sparse matrix is okay (non-nested openMP). For -DOMP_LIB=TBB, nested openMP + TBB MKL is okay.

-DTBB=ON can be combined with any -DOMP_LIB=....

Maximal bond dimension

The default maximal allowed bond dimension per symmetry block is 65535. Adding option -DSMALL_BOND=ON will change this value to 255. Adding option -DLARGE_BOND=ON will change this value to 4294967295.

Release build

The release mode is controlled by CMAKE_BUILD_TYPE:

cmake .. -DCMAKE_BUILD_TYPE=Release

will use optimization flags such as -O3 (default).

cmake .. -DCMAKE_BUILD_TYPE=Debug

enables debug flags.

Supported operating systems and compilers

• Linux + gcc 9.2.0 + MKL 2019
• MacOS 10.15 + Apple clang 12.0 + MKL 2021 (MKL 2019 required for pip install)
• MacOS 10.15 + icpc 2021.1 + MKL 2021
• Windows 10 + Visual Studio 2019 (MSVC 14.28) + MKL 2021

Sometimes, when you have to use block2 together with other python modules (such as pyscf or pyblock), it may have some problem coexisting with each other. In general, change the import order may help. For pyscf, import block2 at the very beginning of the script may help. For pyblock, recompiling block2 use cmake .. -DUSE_MKL=OFF -DBUILD_LIB=ON -OMP_LIB=SEQ -DLARGE_BOND=ON may help.

Usage

The code can either be used as a binary executable or through python interface.

The following are some examples using the python interface.

GS-DMRG

Test Ground-State DMRG (need pyscf module):

python3 -m pyblock2.gsdmrg

FT-DMRG

Test Finite-Temperature (FT)-DMRG (need pyscf module):

python3 -m pyblock2.ftdmrg

LT-DMRG

Test Low-Temperature (LT)-DMRG (need pyscf module):

python3 -m pyblock2.ltdmrg

GF-DMRG

Test Green's-Function (GF)-DMRG (DDMRG++) (need pyscf module):

python3 -m pyblock2.gfdmrg

SI-DMRG

Test State-Interaction (SI)-DMRG (need pyscf module):

python3 -m pyblock2.sidmrg

StackBlock Compatibility

A StackBlock 1.5 compatible user interface can be found at pyblock2/driver/block2main. This script can work as a replacement of the StackBlock binary, with a few limitations and some extensions. The format of the input file dmrg.conf is identical to that of StackBlock 1.5. See docs/driver.md for detailed documentations for this interface. Examples using this interface can be found at tests/driver.

Input File (block2 style)

Example input file for binary executable build/block2:

rand_seed = 1000
memory = 4E9
scratch = ./scratch

pg = c1
fcidump = data/HUBBARD-L16.FCIDUMP
n_threads = 4
qc_type = conventional

# print_mpo
print_mpo_dims
print_fci_dims
print_mps_dims

bond_dims = 500
noises = 1E-6 1E-6 0.0

center = 0
dot = 2

n_sweeps = 10
tol = 1E-7
forward = 1

noise_type = perturbative
trunc_type = physical

To run this example:

./build/block2 input.txt

Using C++ Interpreter cling

Since block2 is designed as a header-only C++ library, it can be conveniently executed using C++ interpreter cling (which can be installed via anaconda) without any compilation. This can be useful for testing samll changes in the C++ code.

Example C++ code for cling can be found at tests/cling/hubbard.cl.