tnpy

Documentation |

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.

Requirments

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

• jcmgray/quimb
• google/Tensornetwork
• primme/primme

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.

Installation

• using Docker

  docker run --rm -it tanlin2013/tnpy
  

• using pip:

  pip install tnpy
  

  for the latest release, or

  pip install git+https://github.com/tanlin2013/tnpy@main
  

  for the development version.

Documentation

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
           self.delta = delta
   
       def _elem(self, site: int) -> np.ndarray:
           Sp, Sm, Sz, I2, O2 = SpinOperators()
           return np.array(
               [[I2, -0.5 * Sp, -0.5 * Sm, -self.delta * Sz, O2],
                [O2, O2, O2, O2, Sm],
                [O2, O2, O2, O2, Sp],
                [O2, O2, O2, O2, Sz],
                [O2, O2, O2, O2, I2]]
           )
        
       @property
       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(
       mpo=model.mpo,
       chi=chi
   )
   fdmrg.update(tol=1e-8)
   

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