ALF

Official Resources

• Homepage: https://alf.physik.uni-wuerzburg.de/
• Repository: https://git.physik.uni-wuerzburg.de/ALF/ALF
• Documentation: https://alf.physik.uni-wuerzburg.de/Documentation/
• License: GPL-3.0

Overview

ALF (Algorithms for Lattice Fermions) is a high-performance, open-source software package designed for Quantum Monte Carlo (QMC) simulations of strongly correlated fermion systems. It specifically implements the Auxiliary-Field QMC (AFQMC) method (also known as Determinantal QMC) to solve a wide class of lattice models at finite temperature or in the ground state (projective). Its key strength lies in its generality: users can define arbitrary Hamiltonians writable in terms of single-body and squared single-body operators.

Scientific domain: Strongly Correlated Electrons, Lattice Gauge Theory Target user community: Theorists studying Hubbard, Kondo, and topological phase transitions

Theoretical Methods

• Method: Auxiliary-Field Quantum Monte Carlo (AFQMC) / Determinantal QMC.
• Transformations: Trotter-Suzuki decomposition for imaginary time and Hubbard-Stratonovich transformation to decouple interactions.
• Ensembles:
  • Finite Temperature (Grand Canonical).
  • Projective (Zero Temperature / Canonical).
• Stabilization: Matrix decomposition stabilization for long imaginary time propagation.

Capabilities

• Models:
  • Hubbard Model (single/multi-orbital).
  • Kondo Lattice Model.
  • Periodic Anderson Model.
  • $Z_2$ Lattice Gauge Theories.
  • User-defined generic Hamiltonians.
• Observables:
  • Equal-time and time-displaced Green's functions.
  • Spin and charge susceptibilities.
  • Renyi Entanglement Entropy.
  • Superconducting pairing correlations.
• Analysis: Stochastic Maximum Entropy (MaxEnt) for analytic continuation to real frequencies.

Key Strengths

• Versatility: Unlike many QMC codes hardwired for the Hubbard model, ALF provides a generic interface (Hamiltonian_interface) to defining any suitable interacting model.
• Optimized: Comparison-free Fortran implementation with MPI parallelism for massive sampling.
• Documentation: Extensive documentation and tutorials provided by the Würzburg group.

Inputs & Outputs

• Inputs:
  • parameters file: Lattice size, temperature, interaction strength $U$.
  • Hamiltonian definition (Fortran modules).
• Outputs:
  • Data files for observables (bins for error analysis).
  • Python scripts (pyALF) for post-processing and plotting.

Interfaces & Ecosystem

• pyALF: A Python interface to manage simulation workflows, generating input files and analyzing results.
• HDF5: Optional support for structured data output.

Performance Characteristics

• Scaling:
  • Linear with inverse temperature $\beta$.
  • Cubic $O(N^3)$ with system volume $N$ (number of orbitals).
• Parallelism: MPI parallelization over Markov chains (embarrassingly parallel sampling).

Comparison with Other Codes

• vs. QUEST: QUEST is another major DQMC code. ALF is arguably more modern in its software engineering (Fortran 2003 objects) and offers a more generalized Hamiltonian interface.
• vs. ALPS: ALPS offers a suite of solvers (including QMC); ALF is a specialized, deep tool for AFQMC with features like projective algorithms and entanglement entropy that standard ALPS applications might lack.

Application Areas

• Quantum Criticality: Studying phase transitions in heavy fermion systems.
• Topological Phases: Simulating topological insulators with interactions (Kane-Mele-Hubbard).
• Graphene: Hubbard model on honeycomb lattices.

Community and Support

• Development: University of Würzburg (Fakher Assaad group).
• Source: GitLab (University hosted).

Verification & Sources

• Website: https://alf.physik.uni-wuerzburg.de/
• Primary Publication: T. C. Lang et al., "ALF: The algorithms for lattice fermions package", SciPost Phys. (2019).
• Verification status: ✅ VERIFIED
  • Active and well-supported community code.