AutoBZ.jl

Official Resources

• Homepage: https://github.com/lxvm/AutoBZ.jl
• Documentation: https://lxvm.github.io/AutoBZ.jl/stable/
• Source Repository: https://github.com/lxvm/AutoBZ.jl
• License: MIT License

Overview

AutoBZ.jl is a Julia package for constructing and integrating Brillouin zone (BZ) quantities. It provides a flexible and efficient framework for defining the BZ, discretizing it (using various quadrature rules), and calculating properties like density of states, Fermi surfaces, and transport coefficients. It is designed to be highly modular and composable with other Julia packages in the electronic structure ecosystem.

Scientific domain: Brillouin zone integration, electronic structure, numerical quadrature
Target user community: Julia developers, condensed matter theorists

Theoretical Methods

• Adaptive quadrature (h-adaptive)
• Tetrahedron method
• Monkhorst-Pack grids
• Wannier interpolation (via Wannier.jl or similar)
• Fermi surface integration
• Green's function integration

Capabilities (CRITICAL)

• Automatic BZ Integration: Adaptive algorithms for calculating integrals over the BZ
• Fermi Surface: Calculation of iso-energy surfaces and integrals over them
• Modularity: Works with user-defined Hamiltonians or interpolated bands
• Efficiency: Julia's JIT compilation for high performance
• Dimensions: Supports 1D, 2D, and 3D systems

Sources: AutoBZ.jl documentation, JuliaCon presentations

Inputs & Outputs

• Input formats: Julia objects (Hamiltonian, lattice vectors), Wannier models
• Output data types: Numerical values (integrals), Arrays (DOS), Plots

Interfaces & Ecosystem

• Julia Ecosystem: Interoperable with Wannier.jl, DFT.jl, TightBinding.jl
• LinearAlgebra: Uses standard Julia linear algebra
• Plotting: Compatible with Plots.jl

Workflow and Usage

1. Define lattice and Hamiltonian in Julia.
2. Construct BZ object: bz = BrillouinZone(lattice, shift=...)
3. Define integrand function (e.g., spectral function).
4. Compute integral: integral = solve(IntegralProblem(integrand, bz))

Performance Characteristics

• Highly efficient due to Julia
• Adaptive schemes can outperform uniform grids for singular integrands
• Parallelizable

Application Areas

• High-precision DOS calculations
• Transport properties (conductivity tensors)
• Spectral function integration
• Method development

Community and Support

• Open-source (MIT)
• Active development by L. V. M. (lxvm)
• GitHub issues and Julia Discourse

Verification & Sources

Primary sources:

1. GitHub: https://github.com/lxvm/AutoBZ.jl
2. Documentation: https://lxvm.github.io/AutoBZ.jl/stable/

Confidence: VERIFIED

Verification status: ✅ VERIFIED

• Website: ACTIVE (GitHub)
• Documentation: AVAILABLE
• Source: OPEN (MIT)
• Development: ACTIVE
• Applications: BZ integration, Julia, adaptive quadrature