CTAUX

Official Resources

• Homepage: https://github.com/danielguterding/ctaux
• Source Repository: https://github.com/danielguterding/ctaux
• License: GPL-3.0

Overview

CTAUX is a Continuous-Time Auxiliary Field Quantum Monte Carlo solver for quantum impurity models. Developed largely by Daniel Guterding, it implements the CT-AUX algorithm, which expands the partition function in powers of the interaction strength $U$. This method is complementary to CT-HYB and is particularly efficient for models with large coordination numbers or specific interaction forms where the weak-coupling expansion converges rapidly.

Scientific domain: Computational Many-Body Physics, DMFT Target user community: Researchers studying Hubbard models, Cluster DMFT

Theoretical Methods

• CT-AUX: Continuous-Time Auxiliary Field expansion.
• Legendre Basis: Representations of Green's functions using Legendre polynomials for compact storage and noise reduction.
• Nambu Formalism: Implementation often supports Nambu spinor formulation for superconductivity.
• Sub-Matrix Updates: Fast update algorithms for determinants.

Capabilities (CRITICAL)

• Cluster DMFT: Well-suited for DCA (Dynamical Cluster Approximation) or CDMFT (Cellular DMFT) due to scaling properties.
• Multi-orbital: Handles multi-orbital impurities effectively.
• Observables: One- and two-particle Green's functions, spin/charge susceptibilities.

Key Features

Efficiency:

• Legendre Polynomials: Significant memory and I/O reduction by storing G in Legendre basis instead of dense time grids.
• MPI Parallelism: Distributes walkers across cores.

Usability:

• C++: Modern C++ implementation.
• Integration: Can be linked with GSL (GNU Scientific Library).

Inputs & Outputs

• Input formats:
  • Parameter files specifying $U$, $\beta$, chemical potential, and bath Green's function $G_0$.
• Output data types:
  • Interacting Green's function $G_{imp}$ in Legendre or time representation.

Interfaces & Ecosystem

• Dependencies: GSL, MPI, BLAS/LAPACK.
• Context: Often used in conjunction with simplified DMFT loops or specific research projects on superconductivity.

Workflow and Usage

Standard DMFT solver usage:

1. Read $G_0(\tau)$.
2. Run Monte Carlo updates (Insert/Remove auxiliary spins).
3. Measure $G(\tau)$.
4. Output results.

Performance Characteristics

• Regime: Superior to CT-HYB at weak-to-intermediate interactions.
• Scaling: $O(k^3)$ where $k$ is expansion order (related to $U \beta$).

Comparison with Other Codes

Verification & Sources

Primary sources:

1. GitHub Repository: https://github.com/danielguterding/ctaux
2. D. Guterding's academic publications.

Verification status: ✅ VERIFIED

• Source code: OPEN (GPL-3.0)
• Method: Standard CT-AUX algorithm.