xdiag

Official Resources

• Homepage: https://github.com/awietek/xdiag
• Documentation: https://awietek.github.io/xdiag/
• Source Repository: https://github.com/awietek/xdiag (and https://github.com/awietek/XDiag.jl)
• License: Apache License 2.0

Overview

xdiag is a modern, high-performance software package for the Exact Diagonalization (ED) of quantum many-body systems. Created by Alexander Wietek, it features a dual-language architecture: a highly optimized C++ core for computational efficiency and a Julia wrapper (XDiag.jl) for a user-friendly, high-level interface. It is designed to solve generic spin, boson, and fermion models on arbitrary geometries, exploiting symmetries to reach the largest possible system sizes.

Scientific domain: Quantum Many-Body Physics, Strongly Correlated Systems, Magnetism Target user community: Theorists using ED for spectral functions, ground states, and time evolution

Theoretical Methods

• Exact Diagonalization: Full or iterative (Lanczos/Davidson) diagonalization of sparse Hamiltonians.
• Symmetries:
  • Translation: Momentum conservation ($k$-blocks).
  • Point Group: Irreducible representations of lattice symmetries.
  • U(1) / SU(2): Conservation of particle number and spin projection $S_z$.
• Sublattice Coding: Efficient state representation for spin systems.

Capabilities (CRITICAL)

• Hilbert Spaces: Supports Spin-1/2, Spin-S, t-J, Fermion (Hubbard), and Boson models.
• General Hamiltonians: Flexible input for arbitrary interaction terms (bond-dependent, long-range).
• Large Systems: Uses distributed memory (MPI) and shared memory (OpenMP) parallelism to solve systems beyond trivial sizes (e.g., 40+ spins).
• Time Evolution: Real-time and Imaginary-time evolution algorithms.
• Spectral Functions: Calculation of $A(k, \omega)$ and dynamical structure factors.

Key Features

Architecture:

• C++ Core (libxdiag): Implements fast state lookup (Lin tables), matrix-vector multiplication, and parallelization.
• Julia Interface: Seamless usage from Julia, allowing easy plotting and post-processing.

Algorithms:

• Distributed Hashing: Efficient parallelization of state space across nodes without full replication.
• Iterative Solvers: Bindings to fast eigensolvers (e.g., Primme or custom Lanczos implementations).

Inputs & Outputs

• Input formats:
  • Julia scripts defining the Coupling, Site, and Geometry.
  • Input files (TOML/JSON) if using the C++ executable directly.
• Output data types:
  • Eigenvalues and Eigenvectors.
  • HDF5 files for heavy data storage.

Interfaces & Ecosystem

• Dependencies: C++17 compiler, MPI, BLAS/LAPACK.
• Julia: XDiag.jl registered in Julia General registry.

Workflow and Usage

Julia Example:

using XDiag
block = Spinhalf(N=16, n_up=8)
ops = OpSum()
ops += "Sz", 1, "Sz", 2
H = Hamiltonian(ops, block)
eigs, vecs = eigsolve(H)

Performance Characteristics

• Speed: State-of-the-art implementation using bit-manipulation and optimized lookup tables.
• Scaling: Scales to supercomputing clusters via MPI.

Comparison with Other Codes

Verification & Sources

Primary sources:

1. GitHub Repository: https://github.com/awietek/xdiag
2. Documentation: https://awietek.github.io/xdiag/
3. Publication: "XDiag: A high-performance exact diagonalization library" (referenced in SciPost/arXiv).

Verification status: ✅ VERIFIED

• Source code: OPEN (Apache 2.0)
• Authors: A. Wietek (Flatiron Institute).
• Quality: Professional-grade research software.