Welcome to \({\mathcal H}\Phi\)’s documentation!

\({\mathcal H}\Phi\) is a numerical solver package for quantum lattice models based on the exact diagonalization method with parallel computing support. See What is {\mathcal H}\Phi? for details.

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You can download software and source codes of \({\mathcal H}\Phi\) from GitHub page or release page.

Contents

• 1. What is \({\mathcal H}\Phi\)?
  • 1.1. What is \({\mathcal H}\Phi\)?
    • 1.1.1. License
    • 1.1.2. Copyright
    • 1.1.3. Contributors
  • 1.2. Operating environment
• 2. How to use \({\mathcal H}\Phi\)
  • 2.1. Prerequisite
  • 2.2. Installation
  • 2.3. Directory structure
  • 2.4. Basic usage
    • 2.4.1. Standard mode
    • 2.4.2. Expert mode
    • 2.4.3. Creating input files for Expert mode
    • 2.4.4. Setting the process number for MPI/hybrid parallelization
    • 2.4.5. Printing version ID
  • 2.5. Troubleshooting
    • 2.5.1. Quick Reference
    • 2.5.2. Detailed Solutions for Common Errors
• 3. Tutorial
  • 3.1. Quick guide to Standard mode
    • 3.1.1. Heisenberg model
    • 3.1.2. Other tutorials
  • 3.2. Quick guide to Expert mode
    • 3.2.1. File list for input files
    • 3.2.2. Files for basic parameters
    • 3.2.3. Files for constructing Hamiltonian
    • 3.2.4. Setting output components
    • 3.2.5. Running
  • 3.3. Fourier transformation of correlation functions
• 4. File specification
  • 4.1. Input files for Standard mode
    • 4.1.1. Parameters for the type of calculation
    • 4.1.2. Parameters for the lattice
    • 4.1.3. Parameters for conserved quantities
    • 4.1.4. Parameters for the Hamiltonian
    • 4.1.5. Parameters for the numerical condition
    • 4.1.6. Parameters for the dynamical Green’s function
    • 4.1.7. Parameters for time-evolution
  • 4.2. Input files for Expert mode
    • 4.2.1. Quick Reference
    • 4.2.2. Detailed Specifications
  • 4.3. Output files
    • 4.3.1. Quick Reference
    • 4.3.2. Detailed Specifications
• 5. Algorithm
  • 5.1. Lanczos method
    • 5.1.1. Details of Lanczos method
    • 5.1.2. Inverse iteration method
    • 5.1.3. Details of implementation
  • 5.2. Full Diagonalization method
    • 5.2.1. Overview
    • 5.2.2. Finite-temperature calculations
  • 5.3. Finite-temperature calculations by the TPQ method
    • 5.3.1. Details of implementation
  • 5.4. Dynamical Green’s function
  • 5.5. Real time evolution method
  • 5.6. Bogoliubov representation
• 6. Technical Details
  • 6.1. Hilbert Space Construction
    • 6.1.1. Bit Representation
    • 6.1.2. State Indexing
    • 6.1.3. Symmetry Restrictions
    • 6.1.4. List Arrays
  • 6.2. MPI Parallelization
    • 6.2.1. Overview
    • 6.2.2. Site Classification
    • 6.2.3. MPI Communication Patterns
    • 6.2.4. Batched MPI Communication
    • 6.2.5. SpinlessFermion Off-diagonal Two-body Green’s Function
    • 6.2.6. Behavior of MPI-required Tests (ctest)
    • 6.2.7. Fermion Sign
    • 6.2.8. Process Number Requirements
  • 6.3. OpenMP Parallelization
    • 6.3.1. Overview
    • 6.3.2. Parallelized Operations
    • 6.3.3. Thread-safe Implementation
    • 6.3.4. Setting the Number of Threads
    • 6.3.5. Performance Considerations
  • 6.4. Memory Management
    • 6.4.1. Memory Requirements
    • 6.4.2. Memory Allocation
    • 6.4.3. Estimating Memory Usage
    • 6.4.4. Memory Optimization Strategies
    • 6.4.5. Common Memory Issues
  • 6.5. Numerical Precision
    • 6.5.1. Floating-Point Representation
    • 6.5.2. Sources of Numerical Error
    • 6.5.3. Convergence Criteria
    • 6.5.4. Setting Convergence Thresholds
    • 6.5.5. Validation and Testing
    • 6.5.6. Recommendations
  • 6.6. Restart Mechanism
    • 6.6.1. Overview
    • 6.6.2. Restart Files
    • 6.6.3. Input/Output Settings
    • 6.6.4. Usage Examples
    • 6.6.5. File Format
    • 6.6.6. MPI Considerations
    • 6.6.7. Common Issues
    • 6.6.8. Best Practices
• 7. Related Tools
  • 7.1. HPhi/mVMC Fourier-Transformation utility
    • 7.1.1. Overview
    • 7.1.2. Tutorial
    • 7.1.3. File format
    • 7.1.4. Behavior of greenr2k utility
    • 7.1.5. Contact
  • 7.2. RESPACK Interface
    • 7.2.1. Overview
    • 7.2.2. Tutorial
    • 7.2.3. Input parameters for Standard mode
    • 7.2.4. File format
    • 7.2.5. Contact
• 8. Acknowledgement