Welcome to PyTeNet’s documentation!¶
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>
Tutorials¶
The following tutorials provide an introduction to the main concepts and features of PyTeNet:
Indices and tables¶
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. SchollwöckThe density-matrix renormalization group in the age of matrix product states
- J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, F. VerstraeteUnifying time evolution and optimization with matrix product states
- I. P. McCullochFrom density-matrix renormalization group to matrix product states
- T. BarthelPrecise evaluation of thermal response functions by optimized density matrix renormalization group schemes