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Tensor Network algorithms implemented in python.

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This project is a python implementation of Tensor Network, a numerical approach to quantum many-body systems.

tnpy is built on top of quimb, along with TensorNetwork for tensor contractions, with optimized support for various backend engines (TensorFlow, JAX, PyTorch, and Numpy). For eigen-solver we adopt primme, an iterative multi-method solver with preconditioning.

Currently, we support Matrix Product State (MPS) algorithms, with more are coming...

  • Finite-sized Density Matrix Renormalization Group (fDMRG)
  • Tree tensor Strong Disorder Renormalization Group (tSDRG)

fDMRG & tSDRG are on alpha-release. For others, please expect edge cases.


See pyproject.toml for more details. But these two are essential building blocks.

Regarding any installation problems with Primme, please refer to Primme official. Also, it's required to have lapack and blas installed in prior to Primme.


  • using Docker

    docker run --rm -it tanlin2013/tnpy
  • using pip:

    pip install tnpy

    for the latest release, or

    pip install git+

    for the development version.


For details about tnpy, see the reference documentation.

Getting started

  1. Defining the Matrix Product Operator of your model as a Callable function with argument site of the type int, e.g. the function _elem(self, site) below. The MPO class then accepts the Callable as an input and constructs a MPO object.

    import numpy as np
    from tnpy.operators import SpinOperators, MPO
    from tnpy.finite_dmrg import FiniteDMRG
    class XXZ:
        def __init__(self, N: int, delta: float) -> None:
            self.N = N
   = delta
        def _elem(self, site: int) -> np.ndarray:
            Sp, Sm, Sz, I2, O2 = SpinOperators()
            return np.array(
                [[I2, -0.5 * Sp, -0.5 * Sm, * Sz, O2],
                 [O2, O2, O2, O2, Sm],
                 [O2, O2, O2, O2, Sp],
                 [O2, O2, O2, O2, Sz],
                 [O2, O2, O2, O2, I2]]
        def mpo(self) -> MPO:
            return MPO(self.N, self._elem)
  2. Call the algorithm to optimize the state.

    N = 100  # length of spin chain
    chi = 60  # virtual bond dimension 
    model = XXZ(N, delta)
    fdmrg = FiniteDMRG(
  3. Compute any physical quantities whatever you want from the obtained state. The resulting MPS is of the type tensornetwork.FiniteMPS, see here for more details.

    my_mps = fdmrg.mps

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