ExactDiagonalization.jl

Official Resources

• Homepage: https://github.com/Quantum-Many-Body/ExactDiagonalization.jl
• Documentation: https://quantum-many-body.github.io/ExactDiagonalization.jl/dev/
• Source Repository: https://github.com/Quantum-Many-Body/ExactDiagonalization.jl
• License: MIT License

Overview

ExactDiagonalization.jl is a comprehensive Julia package for the exact diagonalization of quantum many-body systems. It serves as the ED engine within the QuantumLattices.jl ecosystem. It provides a unified interface to solve bosonic, fermionic, and spin models defined using the symbolic operator algebra of QuantumLattices. It supports both full diagonalization (for small systems/thermal states) and iterative methods (Lanczos/Arnoldi) for ground states and low-lying excitations.

Scientific domain: Condensed Matter Theory, Quantum Magnetism, Strongly Correlated Systems Target user community: Users of the QuantumLattices.jl framework

Theoretical Methods

• Symbolic Operator Mapping: Automatic conversion of symbolic Hamiltonians (from QuantumLattices) to matrix representations.
• Matrix Diagonalization: Wrapper around Julia's Eigen (dense) and Arpack (sparse) solvers.
• Thermodynamics: Calculation of thermal averages via full spectrum or trace estimations.
• Dynamical Correlations: Kubo formula and Lehmann representation for structure factors and susceptibilities.

Capabilities (CRITICAL)

• Generic Models: Supports Spins, Fermions, Bosons, and mixtures.
• Unified Workflow: Seamless integration with the lattice generation and model definition of QuantumLattices.jl.
• Observables: Automated calculation of local observables and correlation functions.
• Path Integral: Some support for path integral formulations (referenced in ecosystem).

Key Features

Ecosystem Integration:

• QuantumLattices.jl: Relies on this for geometry (UnitCell, Lattice) and Algebra (Hilbert space).
• Extensibility: Part of a modular suite including DMRG and QMC codes under Quantum-Many-Body.

Algorithms:

• ED: Full diagonalization for thermodynamic properties.
• Krylov: Iterative solvers for large sparse matrices.

Inputs & Outputs

• Input formats:
  • Julia scripts using Lattice, Hilbert, and Hamiltonian objects from QuantumLattices.
• Output data types:
  • Eigen objects (values/vectors).
  • DataFrames or Dictionaries of results.

Interfaces & Ecosystem

• Dependencies: QuantumLattices.jl, SparseArrays, LinearAlgebra, KrylovKit.
• Sister Packages: DMRG.jl, QuantumMC.jl.

Workflow and Usage

using QuantumLattices, ExactDiagonalization
lattice = Lattice(...)
hilbert = Hilbert(site=>Spin{1//2}() for site in lattice)
H = Hamiltonian(...)
ed = ED(lattice, hilbert, H)
solve!(ed)

Performance Characteristics

• Speed: Efficient construction of matrices from symbolic rules; standard solver performance.
• Versatility: Prioritizes generality over extreme optimization for one specific model type.

Comparison with Other Codes

Verification & Sources

Primary sources:

1. GitHub Repository: https://github.com/Quantum-Many-Body/ExactDiagonalization.jl
2. Documentation: https://quantum-many-body.github.io/ExactDiagonalization.jl/dev/

Verification status: ✅ VERIFIED

• Source code: OPEN (MIT)
• Ecosystem: Core component of Quantum-Many-Body organization.