CT-QMC

Official Resources

• Homepage: Multiple implementations (w2dynamics primary reference)
• Documentation: See specific implementations
• Source Repository: https://github.com/w2dynamics/w2dynamics (w2dynamics)
• License: Varies by implementation

Overview

CT-QMC (Continuous-Time Quantum Monte Carlo) is a general term for the family of continuous-time quantum Monte Carlo algorithms used as impurity solvers in DMFT. This includes CT-HYB, CT-INT, CT-AUX, and other variants. The term CT-QMC often refers generically to these methods, with w2dynamics being a major implementation providing multiple CT-QMC algorithms.

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

Theoretical Methods

• Continuous-time quantum Monte Carlo (general family)
• Hybridization expansion (CT-HYB)
• Interaction expansion (CT-INT)
• Auxiliary field expansion (CT-AUX)
• Segment representation
• Worm sampling algorithms
• Stochastic methods for impurity problems

Capabilities (CRITICAL)

Note: CT-QMC is a FAMILY OF ALGORITHMS, not single software

Major implementations:

• w2dynamics: Comprehensive CT-QMC package (CT-HYB, CT-INT)
• TRIQS/cthyb: CT-HYB variant
• iQIST: Multiple CT-QMC algorithms
• ALPS: CT-HYB implementation
• ComCTQMC: GPU-accelerated CT-QMC

General capabilities (algorithm-dependent):

• Multi-orbital impurity problems
• Temperature-dependent calculations
• Various interaction types
• Green's functions and observables
• Statistical sampling methods

Sources: Master list notes: "VERIFIED - w2dynamics solver", CT-QMC family widely used

Inputs & Outputs

Implementation-dependent: Each variant has specific I/O

Common elements:

• Input: Hybridization/Weiss functions, interactions, temperature
• Output: Green's functions, self-energies, occupations

Interfaces & Ecosystem

• w2dynamics: Complete CT-QMC solver package
• TRIQS: CT-HYB via TRIQS/cthyb
• DCore: Interfaces to multiple CT-QMC solvers
• solid_dmft: Can use various CT-QMC implementations
• DMFT frameworks: Standard impurity solver approach

Limitations & Known Constraints

• Computational cost scales with inverse temperature
• Sign problem in certain regimes
• Statistical errors from Monte Carlo
• Algorithm-specific limitations
• Memory intensive for large problems
• Requires substantial compute resources

Comparison of CT-QMC Variants

Verification & Sources

Primary sources:

1. w2dynamics: https://github.com/w2dynamics/w2dynamics
2. E. Gull et al., Rev. Mod. Phys. 83, 349 (2011) - CT-QMC review
3. A. N. Rubtsov et al., Phys. Rev. B 72, 035122 (2005) - CT-INT
4. P. Werner et al., Phys. Rev. B 74, 155107 (2006) - CT-HYB
5. Master list: "VERIFIED - w2dynamics solver"

Secondary sources:

1. Multiple CT-QMC implementations
2. Standard in DMFT community
3. Extensive literature on CT-QMC methods

Confidence: VERIFIED - Family of algorithms with many implementations

Verification status: ✅ VERIFIED as ALGORITHM FAMILY

• Status: Family of algorithms, not single software
• Multiple implementations: CONFIRMED
• w2dynamics: Major reference implementation
• Widely used in DMFT: CONFIRMED
• Users should specify which CT-QMC variant