MoirePy: Twist It, Solve It, Own It!

MoirePy is a FOSS Python library for simulating moire lattices with a clean, highly Pythonic API. The performance-critical backend is written in Rust, which keeps large lattice generation and Hamiltonian assembly fast while preserving a Python-first workflow.

It is designed to be easy to use while remaining fully flexible. You can define custom lattice geometries, program arbitrary hopping functions, and build tight-binding Hamiltonians in both real space and k-space, with support for open (OBC) and periodic (PBC) boundary conditions. Generate your lattice and Hamiltonian in MoirePy, then export to the tools you already use (like Kwant, NumPy, SciPy, and related ecosystems) and keep your workflow.

• Documentation: https://jabed-umar.github.io/MoirePy/
  
• Github Repository: https://github.com/jabed-umar/MoirePy
  
• PyPI page: https://pypi.org/project/moirepy/

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Why MoirePy

• Plug and play: Build in MoirePy, continue in your current stack: Kwant, NumPy, SciPy etc.
• Fast by default: Rust backend + optimized core algorithms.
• Flexible models: Custom geometry, orbitals, and hoppings.
• Multiple modes: Real-space/k-space and OBC/PBC supported.
• Easy onboarding: Pythonic API and web tools for quick tinkering.

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Philosophy

• Not a workflow replacement: Use MoirePy where it shines, then export to Kwant, NumPy, SciPy, and more.
• Do one thing and do it well: Focus on robust and fast moire lattice simulation and Hamiltonian generation.
• Power to you: If it is mathematically possible, you can build it. No questions asked.
• Learn by doing: Explore fast, and reproduce well-known paper systems.

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Installation

pip install moirepy

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Quick Example: Twisted Bilayer Graphene

import numpy as np
import matplotlib.pyplot as plt
from moirepy import BilayerMoireLattice, HexagonalLayer

# Define a twisted bilayer moiré lattice
lattice = BilayerMoireLattice(
    latticetype=HexagonalLayer,
    # you choose the next 4 values based on the twist angle using this tool:
    # Angle-Value Calculator: https://jabed-umar.github.io/MoirePy/theory/avc/
    ll1=3, ll2=4, ul1=4, ul2=3,
    n1=1, n2=1,
)

# Visualize the lattice
lattice.plot_lattice()
plt.show()

ham = lattice.generate_hamiltonian(
    tll=1, tuu=1,
    tlu=1, tul=1,
    tlself=0, tuself=0
)  # returns scipy sparse matrix

print(ham.shape)

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Benchmark: Why This Is Fast

Basic benchmark snapshots using Twisted Bilayer Graphene (TBG) as a test case, benchmarked on a laptop with a 12th Gen Intel Core i5 (performance cores).

Experiment 1: Full Pipeline

This includes lattice generation plus Hamiltonian assembly. Even at around 160k lattice points, the full pipeline is about 620 ms. For context, configurations near the magic angle ($\sim 1.1^\circ$) typically have just around 5-6k lattice points.

Experiment 2: Subsequent Hamiltonian Generation

After setup, Hamiltonian generation is much faster. At around 160k lattice points, it is about 15 ms. This is the speed profile we optimize for: heavy setup once, then fast repeated builds. Memory usage in these runs is negligible relative to typical laptop RAM.

For more comprehensive performance benchmarks, visit this: BENCHMARK

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Contributing

Contributions are welcome.

• Report bugs or request features via issues
• Submit pull requests for improvements
• Add examples, tutorials, or benchmarks

A detailed contributing guide will be added soon.

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Citation

If you use this work in research:

@software{MoirePy2025,
  author = {Mukhopadhyay, Aritra and Umar, Jabed},
  license = {MIT},
  title = {{MoirePy: Python package for efficient atomistic simulation of moiré lattices}},
  url = {https://github.com/jabed-umar/MoirePy}
}