gharib85/pytenet

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 (real and imaginary)
generate vector / matrix representations of matrix product states / operators
Krylov subspace methods for local operations
one-site local energy minimization using Lanczos iteration
built-in support for additive quantum numbers

Installation

To install PyTeNet, download the source code and run python setup.py install from within the main PyTeNet directory, or add the pytenet/ subfolder to your Python search path.

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 christian.b.mendl@gmail.com

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

U. Schollwöck

The density-matrix renormalization group in the age of matrix product states

Ann. Phys. 326, 96-192 (2011) arXiv:1008.3477, DOI
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, DOI
I. P. McCulloch

From density-matrix renormalization group to matrix product states

J. Stat. Mech. (2007) P10014 arXiv:cond-mat/0701428, DOI
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

gharib85 / pytenet