gharib85/tensor_networks

C implementation of tensor networks for quantum simulations: matrix product states and operators, time evolution (using Trotter splitting), ... Reference implementation for testing using Mathematica

Tensor networks for quantum simulations

C code using CBLAS and LAPACKE; Mathematica simulation analysis notebooks as illustration and reference implementation for testing.

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

Quickstart

The code depends on the CBLAS and LAPACKE libraries. These can be installed via sudo apt install libblas-dev liblapacke-dev (on Ubuntu Linux) or similar. Alternatively, the Makefile shows how to use the Intel compiler with MKL.

Call make to build the project. You might have to adapt some parameters in the Makefile beforehand (see the comments there).

The build process generates executable files in the bin subfolder for several types of Hamiltonians and simulation configurations (like computing dynamical correlations or OTOCs). This folder also contains example parameter files. To run the unit tests, cd into the test subfolder and call ./run_tests.

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

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

License

Copyright (c) 2013-2019, 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