ChemTensor

Tensor network algorithms for chemical systems.

This library is written in C and offers a Python 3 interface for simpler accessibility.

Examples

The examples folder contains several demonstrations of the functionalities. Most examples use Jupyter notebooks and the Python interface.

Features

• Matrix product state and operator structures
• Represent common Hamiltonians as MPOs, including molecular Hamiltonians
• General MPO construction with optimized bond dimensions from a list of operator chains
• Block-sparse tensors based on additive quantum number conservation to implement abelian symmetries
• Single- and two-site DMRG algorithm
• Gradient computation with respect to MPO parameters
• Tree tensor network topologies (work in progress )
• Non-abelian symmetries (work in progress)

Building

The code requires the BLAS, LAPACKE, HDF5 and Python 3 development libraries with NumPy. These can be installed via

• sudo apt install libblas-dev liblapacke-dev libhdf5-dev python3-dev python3-numpy (on Ubuntu Linux)
• brew install openblas lapack hdf5 python3 numpy (on MacOS)

From the project directory, use cmake to build the project:

mkdir build && cd build
cmake ../
cmake --build .

Currently, this will compile the unit tests, which you can run via ./chemtensor_test, as well as the demo examples and Python module library.

Coding style conventions

• Generally, follow the current coding style of the project.
• Naming: lower_case_with_underscores in general (variable, function, and struct names); exceptionally CAPITALIZATION for preprocessor and enum constants.
• Tabs for indentation at the beginning of a line, otherwise whitespace. This ensures that vertical alignment (of, e.g., comments for struct members) is independent of tab size. Avoid trailing whitespace.
• Comments: // for normal comments, /// for Doxygen documentation.
• Put curly braces { } after every if and else (to avoid pitfalls).
• Left-align pointers throughout: int* p instead of int *p.
• Keep the struct and enum keywords in variable types: struct foo f; instead of typedef struct foo { ... } foo_t; foo_t f;.
• Use const for function arguments which are not modified by the function.

References

• U. Schollwöck
  The density-matrix renormalization group in the age of matrix product states
  Ann. Phys. 326, 96-192 (2011) (arXiv:1008.3477)
• J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, F. Verstraete
  Unifying time evolution and optimization with matrix product states
  Phys. Rev. B 94, 165116 (2016) (arXiv:1408.5056)
• C. Krumnow, L. Veis, Ö. Legeza, J. Eisert
  Fermionic orbital optimization in tensor network states
  Phys. Rev. Lett. 117, 210402 (2016) (arXiv:1504.00042)
• G. K.-L. Chan, A. Keselman, N. Nakatani, Z. Li, S. R. White
  Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
  J. Chem. Phys. 145, 014102 (2016) (arXiv:1605.02611)
• J. Ren, W. Li, T. Jiang, Z. Shuai
  A general automatic method for optimal construction of matrix product operators using bipartite graph theory
  J. Chem. Phys. 153, 084118 (2020) (arXiv:2006.02056)