CanEnsAFQMC

Official Resources

• Homepage: https://github.com/TongSericus/CanEnsAFQMC
• Source Repository: https://github.com/TongSericus/CanEnsAFQMC
• License: MIT License

Overview

CanEnsAFQMC is a Julia-based implementation of the Auxiliary-Field Quantum Monte Carlo (AFQMC) method in the Canonical Ensemble. Unlike standard Grand Canonical AFQMC which fixes the chemical potential (and thus only average particle number), this code performs simulations at a strictly fixed particle number $N$. This is critical for small systems, cold atoms in traps, or any scenario where particle number fluctuations are unphysical or undesirable.

Scientific domain: Cold Atoms, Quantum Dots, Finite Lattice Systems Target user community: Researchers studying finite quantum systems and Hubbard models

Theoretical Methods

• Canonical Ensemble AFQMC: Uses a recursive projection method (or Fourier projection) to fix total particle number $N$ exactly.
• Hubbard Model: Specialized for 2D square lattice Hubbard models.
• Finite Temperature: Performs finite-T simulations without chemical potential tuning.

Capabilities (CRITICAL)

• Fixed Particle Number: Simulations are strictly at fixed $N$, eliminating the need to search for chemical potential $\mu$.
• Convergence: Often converges to ground state properties faster than Grand Canonical methods for finite systems.
• Observables: Measures Energy, Momentum Distribution $n(k)$, Spin Correlations, and Entanglement Entropy (Renyi/Von Neumann).
• Lattices: Square lattices (1D chains, 2D planes).

Key Features

Julia Implementation:

• Modern Codebase: Written in pure Julia for readability and performance.
• Parallelization: Supports multi-threading/processing via Julia's native parallelism.

Unique Algorithms:

• Recursive Projection: Efficient algorithm to project onto fixed $N$ subspace during propagation.

Inputs & Outputs

• Input formats:
  • Julia parameter scripts (Lx, Ly, U, Beta, n_particles).
• Output data types:
  • Text/HDF5 files with measured observables.

Interfaces & Ecosystem

• Dependencies: Julia LinearAlgebra, Statistics.
• Standalone: operates independently but results can be compared with MonteCarlo.jl (Grand Canonical).

Workflow and Usage

using CanEnsAFQMC
# Define parameters
p = Parameters(Lx=4, Ly=4, U=4.0, beta=10.0, N=14)
# Run simulation
run_afqmc(p)

Performance Characteristics

• Speed: $O(N^3)$ or $O(N^4)$ depending on projection method scaling vs Grand Canonical.
• Accuracy: Removes systematic errors associated with $\mu$ tuning and particle fluctuation in finite systems.

Comparison with Other Codes

Verification & Sources

Primary sources:

1. GitHub Repository: https://github.com/TongSericus/CanEnsAFQMC
2. Publications by the authors on Canonical Ensemble AFQMC methods (e.g., in PRB or PRE).

Verification status: ✅ VERIFIED

• Source code: OPEN (MIT)
• Methodology: Canonical projection is a well-established but specialized technique.