Pymablock: quasi-degenerate perturbation theory in Python

Pymablock (Python matrix block-diagonalization) is a Python package that constructs effective models using quasi-degenerate perturbation theory. It handles both numerical and symbolic inputs, and it efficiently block-diagonalizes Hamiltonians with multivariate perturbations to arbitrary order.

Building an effective model using Pymablock is a three step process:

• Define a Hamiltonian
• Call pymablock.block_diagonalize
• Request the desired order of the effective Hamiltonian

from pymablock import block_diagonalize

# Define perturbation theory
H_tilde, *_ = block_diagonalize([h_0, h_p], subspace_eigenvectors=[vecs_A, vecs_B])

# Request correction to the effective Hamiltonian
H_AA_4 = H_tilde[0, 0, 4]

Here is why you should use Pymablock:

• Do not reinvent the wheel

  Pymablock provides a tested reference implementation

• Apply to any problem

  Pymablock supports numpy arrays, scipy sparse arrays, sympy matrices and quantum operators

• Speed up your code

  Due to several optimizations, Pymablock can reliably handle both higher orders and large Hamiltonians

For more details see the Pymablock documentation.