pytenet 1.3.0

Tensor network library for quantum simulations

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)
nsites = 10

# construct matrix product operator representation of the
# Heisenberg XXZ Hamiltonian (arguments are nsites, J, \Delta, h)
h_mpo = ptn.heisenberg_xxz_1d_mpo(nsites, 1.0, 0.8, -0.1)
h_mpo.zero_qnumbers()

# initial wavefunction as MPS with random entries
# maximally allowed virtual bond dimensions
b = [1, 2, 4, 8, 16, 28, 16, 8, 4, 2, 1]
psi = ptn.MPS(h_mpo.qsite, [bi*[0] for bi in b], fill="random")
# effectively clamp virtual bond dimension of initial state
b_init = 8
for i in range(nsites):
    psi.a[i][:, b_init:, :] = 0
    psi.a[i][:, :, b_init:] = 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.tdvp_singlesite(h_mpo, 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 [e-mail]

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, Christian B.},
  title   = {{PyTeNet}: A concise {P}ython 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)