CyGutz

Official Resources

• Source Repository: https://github.com/yaoyongxin/CyGutz
• License: Custom Open Source (Ames Lab / Rutgers / DOE - BSD-like)

Overview

CyGutz is a Gutzwiller solver implemented in Cython/Python. It is designed to solve generic tight-binding models with local interactions using the Gutzwiller-Rotationally Invariant Slave-Boson (RISB) method. It optimizes the single Slater determinant and local many-body degrees of freedom simultaneously within the Gutzwiller approximation.

Scientific domain: Strongly correlated electrons, Gutzwiller approximation, Slave-Boson methods Target user community: Researchers studying Hubbard models, tight-binding systems with correlations

Theoretical Methods

• Gutzwiller Approximation
• Rotationally Invariant Slave-Boson (RISB) theory
• Variational Monte Carlo (connection to)
• Tight-Binding models

Capabilities

• Solving generic tight-binding models with local interactions
• Optimizing Gutzwiller variational parameters
• Handling multi-orbital systems
• Calculation of renormalized band structures

Key Strengths

Efficiency:

• Mean-field cost, much cheaper than DMFT or QMC.

Generic Models:

• Can handle general tight-binding Hamiltonians.

Implementation:

• Cython helps in performance while maintaining Python usability.

Inputs & Outputs

• Input formats:
  • Tight-binding parameters (hopping)
  • Interaction parameters (Coulomb U, J)
• Output data types:
  • Renormalized hoppings
  • Quasiparticle weights (Z)
  • Ground state energy
  • Orbital occupations

Interfaces & Ecosystem

• Python: Designed to be used as a Python library/module.

Advanced Features

• Rotationally Invariant: Handles general interaction tensors effectively.
• Simultaneous Optimization: Optimizes both the uncorrelated wavefunction and the projector.

Performance Characteristics

• Speed: Very fast compared to dynamic solvers.
• Scaling: Scales reasonably with system size, limited mainly by the local Hilbert space size for the slave bosons.

Computational Cost

• Low: Mean-field level cost.

Limitations & Known Constraints

• Approximation: It is a static mean-field theory (Gutzwiller), missing dynamic correlations (frequency dependence).
• Accuracy: Good for ground state properties (Fermi surface, mass enhancement) but fails for satellites/incoherent features.

Comparison with Other Codes

• vs DMFT: Cheaper, static, no spectral functions (only quasiparticles).
• vs DFT+U: More flexible treatment of local correlations (screening, mass enhancement).

Verification & Sources

Primary sources:

1. GitHub: https://github.com/yaoyongxin/CyGutz

Verification status: ✅ VERIFIED

• Source code: OPEN