C implementation of tensor networks for quantum simulations: matrix product states and operators, time evolution (using Trotter splitting), ... Reference implementation for testing using Mathematica
Mathematica C Other
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Failed to load latest commit information.
analysis
bin
doc
include
mathematica
src
test
.gitattributes
.gitignore
Doxyfile
Makefile
ReadMe.md

ReadMe.md

Tensor networks for quantum simulations

C with Intel MKL, and Mathematica reference implementation

Features:

  • common operations on tensors of arbitrary dimension
  • MPS and MPO structures
  • built-in support for quantum numbers (U(1) symmetries)
  • construction of common Hamiltonians (Ising, Heisenberg, Fermi-Hubbard, Bose-Hubbard) in 1D, by even-odd splitting or as MPO representation; MPO representation from arbitrary operator chain description
  • imaginary and real-time evolution using even-odd splitting
  • time-dynamical correlation functions and OTOCs at finite temperature
  • one-site and two-site local energy minimization using Lanczos iteration
  • preliminary support for PEPS

Directory structure:

  • mathematica: standalone Mathematica reference implementation, with the core routines in the tn_base.m package
  • include, src: source code of the C implementation
  • test: unit tests for the C implementation, using the Mathematica version as reference
  • doc: documentation of the C code (generated by Doxygen)
  • analysis: simulation analysis notebooks, as illustration

The Mathematica notebooks can be opened by the free CDF player.

License

Copyright (c) 2013-2018, Christian B. Mendl
All rights reserved.
http://christian.mendl.net

This program is free software; you can redistribute it and/or modify it under the terms of the Simplified BSD License http://www.opensource.org/licenses/bsd-license.php

References

  1. U. Schollwöck
    The density-matrix renormalization group in the age of matrix product states
    Ann. Phys. 326, 96-192 (2011) arXiv:1008.3477, DOI
  2. T. Barthel
    Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes
    New J. Phys. 15, 073010 (2013) arXiv:1301.2246, DOI
  3. F. Verstraete, V. Murg, J. I. Cirac
    Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
    Adv. Phys. 57, 143-224 (2008) arXiv:0907.2796, DOI