PyTeNet

PyTeNet is a Python implementation of quantum tensor network operations and simulations within the matrix product state framework, using NumPy to handle tensors.

Example usage for TDVP time evolution:

import pytenet as ptn

# number of lattice sites (1D with open boundary conditions)
L = 10

# construct matrix product operator representation of
# Heisenberg XXZ Hamiltonian (arguments are L, J, \Delta, h)
mpoH = ptn.heisenberg_xxz_mpo(L, 1.0, 0.8, -0.1)
mpoH.zero_qnumbers()

# initial wavefunction as MPS with random entries
# maximally allowed virtual bond dimensions
D = [1, 2, 4, 8, 16, 28, 16, 8, 4, 2, 1]
psi = ptn.MPS(mpoH.qd, [Di*[0] for Di in D], fill='random')
# effectively clamp virtual bond dimension of initial state
Dinit = 8
for i in range(L):
    psi.A[i][:, Dinit:, :] = 0
    psi.A[i][:, :, Dinit:] = 0
psi.orthonormalize(mode='left')

# time step can have both real and imaginary parts;
# for real time evolution use purely imaginary dt!
dt = 0.01 - 0.05j
numsteps = 100

# run TDVP time evolution
ptn.integrate_local_singlesite(mpoH, psi, dt, numsteps, numiter_lanczos=5)
# psi now stores the (approximated) time-evolved state exp(-dt*numsteps H) psi

Features

• matrix product state and operator classes
• construct common Hamiltonians as MPOs, straightforward to adapt to custom Hamiltonians
• convert arbitrary operator chains to MPOs
• TDVP time evolution (single- and two-site, both real and imaginary time)
• generate vector / matrix representations of matrix product states / operators
• Krylov subspace methods for local operations, like local energy minimization
• single- and two-site DMRG algorithm
• built-in support for additive quantum numbers

Installation

To install PyTeNet from PyPI, call

python3 -m pip install pytenet

Alternatively, you can clone the repository and install it in development mode via

python3 -m pip install -e <path/to/repo>

Documentation

The full documentation is available at pytenet.readthedocs.io.

Directory structure

• pytenet: source code of the actual PyTeNet package
• doc: documentation and tutorials
• test: unit tests (might serve as detailed documentation, too)
• experiments: numerical experiments on more advanced, in-depth topics
• paper: JOSS manuscript

Contributing

Feature requests, discussions and code contributions to PyTeNet in the form of pull requests are of course welcome. Creating an issue might be a good starting point. New code should be well documented (Google style docstrings) and unit-tested (see the test/ subfolder). For questions and additional support, fell free to contact [email protected]

Citing

PyTeNet is published in the Journal of Open Source Software - if it's ever useful for a research project please consider citing it:

@ARTICLE{pytenet,
  author = {Mendl, C. B.},
  title = {PyTeNet: A concise Python implementation of quantum tensor network algorithms},
  journal = {Journal of Open Source Software},
  year = {2018},
  volume = {3},
  number = {30},
  pages = {948},
  doi = {10.21105/joss.00948},
}

License

PyTeNet is licensed under the BSD 2-Clause license.

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)
2. 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)
3. I. P. McCulloch

   From density-matrix renormalization group to matrix product states

   J. Stat. Mech. (2007) P10014 (arXiv:cond-mat/0701428)
4. T. Barthel

   Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes

   New J. Phys. 15, 073010 (2013) (arXiv:1301.2246)