quantumhall-matrixelements

quantumhall-matrixelements provides a compact set of kernels and helper objects for common quantum Hall workflows:

• plane-wave Landau-level form factors

• exchange kernels in a Landau-level basis

• symmetric-gauge density, one-body, and pseudopotential building blocks

The documentation is written for users who want correct conventions, equations, and working examples without reading backend internals.

Start from the right page

• Conventions
  • Magnetic-field sign
  • Momentum and magnetic-length units
  • Landau-gauge form factor
  • Exchange kernel
  • Symmetric gauge
  • Coulomb scaling
• Plane-wave workflows
  • Form factors
  • Exchange kernels
  • Repeated Fock applications
  • Backend choice
• Symmetric-gauge workflows
  • Factorized density form factors
  • Haldane pseudopotentials
  • Reconstruct disk two-body matrix elements
  • Central one-body matrix elements
• API Reference
  • Plane-wave and exchange workflows
  • Symmetric-gauge workflows
  • Diagnostics and opposite-field helpers
  • Advanced backend-specific entry points
• Worked examples

Installation

pip install quantumhall_matrixelements

For a local checkout with tests and docs tooling:

pip install -e .[dev,docs]

Minimal example

import numpy as np
from quantumhall_matrixelements import get_exchange_kernels, get_form_factors

q = np.array([0.0, 1.0, 2.0])
theta = np.zeros_like(q)
nmax = 3

F = get_form_factors(q, theta, nmax)
X = get_exchange_kernels(q[1:], theta[1:], nmax)

print(F.shape)  # (3, 3, 3)
print(X.shape)  # (2, 3, 3, 3, 3)

What to expect from the package

• Physical conventions are explicit. The lB scaling, the charge-field sign, and the tensor index order are part of the public contract.

• Large tensors are not hidden behind friendly names. The exchange kernel scales like O(nmax^4) per G, so the compressed APIs matter.

• The default path is meant to be reliable for production calculations, not just toy examples.