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block2 is an efficient and highly scalable implementation of the Density Matrix Renormalization Group (DMRG) for quantum chemistry, based on Matrix Product Operator (MPO) formalism. The code is highly optimized for production level calculation of realistic systems. It also provides plenty of options for tuning performance and new algorithm development.

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.


Tutorial (python interface):

Source code:


  • Huanchen Zhai @hczhai: DMRG and parallelization

  • Henrik R. Larsson @h-larsson: DMRG-MRCI/MRPT and big site

  • Seunghoon Lee @seunghoonlee89: Stochastic perturbative DMRG

  • Zhi-Hao Cui @zhcui: user interface


  • 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

  • Finite-Temperature DMRG (ancilla approach)

  • 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
    • Extracting Determinant/CSF coefficients from MPS

    • Constructing MPS from Determinant/CSF coefficients

  • 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)

  • DMRG with Spin-Orbit Coupling (SOC)
    • 1-step approach (full complex one-MPO and hybrid real/complex two-MPO schemes)

    • 2-step approach

  • 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

User Guide