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. L. Low communication high performance ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics 2021, 154, 224116, doi: 10.1063/5.0050902.
For the large site code, please cite
- Larsson, H. R., Zhai, H., Gunst, K., Chan, G. K. L. Matrix product states with large sites. Journal of Chemical Theory and Computation 2022, 18, 749-762, doi: 10.1021/acs.jctc.1c00957.
You can find a bibtex file in CITATIONS.bib
.
One can install block2
using pip
:
-
OpenMP-only version (no MPI dependence)
pip install block2
-
Hybrid openMP/MPI version (requiring openMPI 4.0.x and
mpi4py
based on the same openMPI library installed)pip install block2-mpi
-
Binary format is prepared via
pip
for python 3.7, 3.8, 3.9, and 3.10 with macOS (x86 and arm64, no-MPI) or Linux (no-MPI/openMPI). If these binaries have some problems, you can use the--no-binary
option ofpip
to force building from source (for example,pip install block2 --no-binary block2
). -
One should only install one of
block2
andblock2-mpi
.block2-mpi
covers all features inblock2
, but its dependence on mpi library can sometimes be difficult to deal with. Some guidance for resolving environment problems can be found in issue #7 and here. -
To install the most recent development version, use:
pip install block2==<version> --extra-index-url=https://block-hczhai.github.io/block2-preview/pypi/ pip install block2-mpi==<version> --extra-index-url=https://block-hczhai.github.io/block2-preview/pypi/
where
<version>
can be some development version number like0.5.1rc14
.
To run a DMRG calculation using the command line interface, 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.
For DMRGSCF calculation, please have a look at the documentation.
Documentation: https://block2.readthedocs.io/en/latest/
Tutorial (python interface): https://block2.readthedocs.io/en/latest/tutorial/hubbard.html
Source code: https://github.com/block-hczhai/block2-preview
- State symmetry
- U(1) particle number symmetry
- SU(2) or U(1) spin symmetry (spatial orbital)
- No spin symmetry (general spin orbital)
- Abelian point group symmetry
- Translational (K point) / 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
- Ground-State DMRG
- 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 / 3PDM / 4PDM
- Transition 1PDM / 2PDM / 3PDM / 4PDM
- 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 coefficients of MPS
- Multi-level parallel DMRG
- Parallelism over sites (2-site only)
- Parallelism over sum of MPOs (distributed)
- Parallelism over operators (distributed/shared memory)
- Parallelism over symmetry sectors (shared memory)
- Parallelism within dense matrix multiplications (MKL)
- DMRG-CASSCF and contracted dynamic correlation
- DMRG-CASSCF (pyscf / openMOLCAS / forte interface)
- DMRG-CASSCF nuclear gradients and geometry optimization (pyscf interface, RHF reference only)
- DMRG-sc-NEVPT2 (pyscf interface, classical approach)
- DMRG-sc-MPS-NEVPT2 (pyscf interface, MPS compression approximation)
- DMRG-CASPT2 (openMOLCAS interface)
- DMRG-cu-CASPT2 (openMOLCAS interface)
- DMRG-MRDSRG (forte interface)
- Stochastic perturbative DMRG
- DMRG with Spin-Orbit Coupling (SOC)
- 1-step approach (full complex one-MPO and hybrid real/complex two-MPO schemes)
- 2-step approach
- 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
- 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.
- 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. L. 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.
- 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.
- Zhai, H., Chan, G. K. A comparison between the one- and two-step spin-orbit coupling approaches based on the ab initio Density Matrix Renormalization Group. The Journal of Chemical Physics 2022, 157, 164108. https://doi.org/10.1063/5.0107805.
- 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.
- 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.
- Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B., Verstraete, F. Unifying time evolution and optimization with matrix product states. Physical Review B 2016, 94, 165116. https://doi.org/10.1103/PhysRevB.94.165116.
- 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.
- 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.
- 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.
- Guo, S., Watson, M. A., Hu, W., Sun, Q., Chan, G. K. L. N-electron valence state perturbation theory based on a density matrix renormalization group reference function, with applications to the chromium dimer and a trimer model of poly (p-phenylenevinylene). Journal of Chemical Theory and Computation 2016, 12, 1583-1591. https://doi.org/10.1021/acs.jctc.5b01225.
- Roemelt, M., Guo, S., Chan, G. K. L. A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions. The Journal of Chemical Physics 2016, 144, 204113. https://doi.org/10.1063/1.4950757.
- Sokolov, A. Y., Guo, S., Ronca, E., Chan, G. K. L. Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes. The Journal of Chemical Physics 2017, 146, 244102. https://doi.org/10.1063/1.4986975.
- Kurashige, Y., Yanai, T. Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: Theory and application to the study of chromium dimer. The Journal of Chemical Physics 2011, 135, 094104. https://doi.org/10.1063/1.3629454.
- Wouters, S., Van Speybroeck, V., Van Neck, D. DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes. The Journal of Chemical Physics 2016, 145, 054120. https://doi.org/10.1063/1.4959817.
- Nakatani, N., Guo, S. Density matrix renormalization group (DMRG) method as a common tool for large active-space CASSCF/CASPT2 calculations. The Journal of Chemical Physics 2017, 146, 094102. https://doi.org/10.1063/1.4976644.
-
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.
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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.
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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.
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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.
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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.
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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.
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Angeli, C., Cimiraglia, R., Malrieu J.-P. N-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants. The Journal of chemical physics 2002, 117, 9138-9153. https://doi.org/10.1063/1.1515317.
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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.
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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.
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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.
-
Larsson, H. R., Zhai, H., Gunst, K., Chan, G. K. L. Matrix product states with large sites. Journal of Chemical Theory and Computation 2022, 18, 749-762. https://doi.org/10.1021/acs.jctc.1c00957.
- 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.
- 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.
- 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.
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).
One can add both the repo root directory and the build
directory into PYTHONPATH
so that import block2
and import pyblock2
will work.
If -DUSE_MKL=ON
is not given, blas
and lapack
are required. Sometimes, the blas
and lapack
function names can contain the extra underscore. Therefore, it is recommended to use -DUSE_MKL=OFF
and -DF77UNDERSCORE=ON
together to prevent this underscore problem. If this generates the undefined reference error, one should try -DUSE_MKL=OFF -DF77UNDERSCORE=OFF
instead.
Use -DUSE_MKL64=ON
instead of -DUSE_MKL=ON
to enable using matrices with 64-bit integer type.
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.
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.
To build unit tests and binary executable (instead of python extension), use the following:
cmake .. -DUSE_MKL=ON -DBUILD_TEST=ON
Adding (optional) option -DTBB=ON
will utilize malloc
from tbbmalloc
.
This can improve multi-threading performance.
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 developers : 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=...
.
For complex integrals / spin-orbit coupling (SOC), extra options -DUSE_COMPLEX=ON
and -DUSE_SG=ON
are required (and the compilation time will increase).
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
.
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.
- Linux + gcc 9.2.0 + MKL 2021.4
- MacOS 10.15 + Apple clang 12.0 + MKL 2021 (MKL 2021.4 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.
The code can either be used as a binary executable or through python interface.
The following are some examples using the python interface.
Test Ground-State DMRG (need pyscf
module):
python3 -m pyblock2.gsdmrg
Test Finite-Temperature (FT)-DMRG (need pyscf
module):
python3 -m pyblock2.ftdmrg
Test Low-Temperature (LT)-DMRG (need pyscf
module):
python3 -m pyblock2.ltdmrg
Test Green's-Function (GF)-DMRG (DDMRG++) (need pyscf
module):
python3 -m pyblock2.gfdmrg
Test State-Interaction (SI)-DMRG (need pyscf
module):
python3 -m pyblock2.sidmrg
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
and docs/source/user/basic.rst
for detailed documentations for this interface.
Examples using this interface can be found at tests/driver
.
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
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 small changes in the C++ code.
Example C++ code for cling
can be found at tests/cling/hubbard.cl
.