CT-HYB

Official Resources

• Homepage: Multiple implementations (TRIQS/cthyb, ALPS/CT-HYB, etc.)
• Documentation: See specific implementations
• Source Repository: Various (TRIQS, ALPS, w2dynamics, etc.)
• License: Varies by implementation

Overview

CT-HYB (Continuous-Time Hybridization Expansion) is an algorithm for solving quantum impurity problems, not a single specific software. It is the most widely used continuous-time quantum Monte Carlo (CTQMC) method in DMFT applications. Multiple implementations exist in different software packages including TRIQS/cthyb, ALPS, w2dynamics, iQIST, and others.

Scientific domain: Quantum impurity solvers, DMFT, CTQMC algorithms
Target user community: Researchers performing DMFT calculations

Theoretical Methods

• Continuous-time quantum Monte Carlo (CTQMC)
• Hybridization expansion algorithm
• Stochastic sampling in imaginary time
• Multi-orbital Anderson impurity model
• Partition function expansion
• Segment picture or matrix formulation

Capabilities (CRITICAL)

Note: CT-HYB is an ALGORITHM implemented in multiple codes:

Primary implementations:

• TRIQS/cthyb: Most widely used, GPL-licensed
• ALPS/CT-HYB: Part of ALPS project
• w2dynamics: Includes CT-HYB solver
• iQIST: Multiple CT-HYB variants
• ComCTQMC: GPU-accelerated version

General capabilities:

• Multi-orbital impurity problems
• General interactions
• Temperature-dependent calculations
• Green's functions and self-energies
• Statistical sampling

Sources: Master list notes: "VERIFIED - TRIQS implementation", algorithm widely implemented

Inputs & Outputs

Depends on implementation: Each code has its own interface

Common inputs: Hybridization functions, interaction parameters Common outputs: Green's functions, self-energies, occupations

Interfaces & Ecosystem

• TRIQS/cthyb: Standard in TRIQS ecosystem
• ALPS: Part of ALPS solvers
• w2dynamics: Integrated CT-HYB
• DCore: Can use various CT-HYB implementations
• Multiple frameworks: Most DMFT codes support CT-HYB

Limitations & Known Constraints

• CTQMC computational cost
• Sign problem in some regimes
• Statistical errors
• Scales with inverse temperature
• Implementation-specific limitations

Comparison with Other Algorithms

Verification & Sources

Primary sources:

1. E. Gull et al., Rev. Mod. Phys. 83, 349 (2011) - CT-HYB review
2. P. Werner and A. J. Millis, Phys. Rev. B 74, 155107 (2006) - Original algorithm
3. TRIQS/cthyb: https://triqs.github.io/cthyb/
4. Master list: "VERIFIED - TRIQS implementation"

Secondary sources:

1. Multiple implementations in major DMFT codes
2. Standard algorithm in DMFT community
3. Hundreds of papers using CT-HYB

Confidence: VERIFIED - Algorithm with multiple implementations

Verification status: VERIFIED as ALGORITHM

• Status: Algorithm/method, not single software
• Multiple implementations: CONFIRMED
• Most common: TRIQS/cthyb
• Widely used in DMFT: CONFIRMED
• Users should specify which implementation