1. Model 1D

The base class for generating an 1-dimensional model where its Hamiltonian can be expressed in Matrix Product Operator (MPO).

tnpy.model.Model1D(n)

param n System size.

1.2. Customize the model

Apart from the built-in models, it’s possible customize the model by implementing tnpy.model.Model1D._elem(), which accepts site (int) as input, and is expected to return a numpy.ndarray.

import numpy as np
from tnpy.operators import SpinOperators
from tnpy.model import Model1D

class XXZ(Model1D):
    def __init__(self, n: int, delta: float):
        self.delta = delta
        super().__init__(n)

    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]]
        )

One can then access the MPO operator by calling tnpy.model.Model1D.mpo, which returns a tnpy.operators.MatrixProductOperator object.

model = XXZ(n=10, delta=0.5)
mpo = model.mpo