PyTeN

PyTeN is a small python3-only tensor network library that can be used to calculate ground-states and do real time evolution of 1d quantum systems.

finite systems:

• ground states using DMRG

• Real time evolution using TEBD or TDVP

• supports MPO encoding of Hamiltonians

  TDVP does currently not support dynamical expansion of the bond dimension

infinite systems

• ground states for translational invariant systems using gradient optimization (https://arxiv.org/abs/1801.02219)
• ground states for translational invariant systems using VUMPS (https://arxiv.org/pdf/1701.07035.pdf)
• ground states for systems with finite unit-cells using IDMRG

the examples folder contains examples of how to use it

Dependencies:

• scipy and numpy installation
• ncon (https://github.com/mhauru/ncon) (ships with this repository)
• matplotlib

Getting Started

Clone the repository and cd to the examples folder:

cd PyTeN/examples

and run the example scripts. HeisMPS.py runs DMRG for a Heisenberg model:

python HeisMPS.py

TEBD.py and TDVP.py calculate the ground state of a N site Heisenberg model, then applies an S+ at the center and evolves the state using TEBD (https://arxiv.org/abs/quant-ph/0301063) or TDVP (https://arxiv.org/abs/1408.5056) algorithm. Run

python TEBD.py
python TDVP.py

to do the evolution.

The above examples-scripts are commented to explain the individual steps and help you to get started with new models.

Getting help

There is currently no documentation, but most methods have docstring explaining what they do.

Prerequisites

You need an numpy and scipy installation. I have tested the code with numpy 1.14.3 and scipy 0.19.0 and 1.1.0. To run the test cases, you additionally need the cython compiler installed on your OS (see below)

Installing

To generate the binary files needed for testing, cd to

cd PyTeN/tests/HeisED

and run

python setup.py build_ext --inplace

This should create a file XXZED.so (or a similar name, depending on the installed c compiler. gcc might throw some warnings at you).

Running the tests

Once the .so file from above is generated, run

python testCasesMPS.py
python DMRGtest.py
python timeevtests.py

which should all finish without error (some warnings may show up).

Extending

New models can be implemented using the MPO formalism. In lib/mpslib/Hamiltonians.py you can find a few examples of how this is done. Any new Hamiltonian should be implemented by declaring a new class. The class should be derived from the base class MPO (see top of Hamiltonians.py). I use the following convention for building nearest neighbor MPOs:

11
O_11
.
.
.
O_N1, O_N2, ..., O_NN, 11

11 and O_ij are local physical operators appearing in the Hamiltonian. Some functions assume that the MPO has such a form (for example the member MPO.twoSiteGate(m,n,tau) for obtaining unitary gates for TEBD), so I strongly advise to conform to this convention.

Authors

• Martin Ganahl If you have any question, suggestions or concerns feel free to drop me an email or use the Issues system.

License

This project is licensed under the MIT License - see the LICENSE.md file for details

Acknowledgments

• Ash Milsted (https://github.com/amilsted/evoMPS)
• Markus Hauru (https://github.com/mhauru/ncon)