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

About \({\mathcal H}\Phi\)

A numerical solver package for a wide range of quantum lattice models including Hubbard-type itinerant electron hamiltonians, quantum spin models, and Kondo-type hamiltonians for itinerant electrons coupled with quantum spins. The Lanczos algorithm for finding ground states and newly developed Lanczos-based algorithm for finite-temperature properties of these models are implemented for parallel computing. A broad spectrum of users including experimental researchers is cordially welcome.

License

This package is distributed under GNU General Public License version 3 (GPL v3) or later.

We kindly ask you to cite the article

Mitsuaki Kawamura, Kazuyoshi Yoshimi, Takahiro Misawa, Youhei Yamaji, Synge Todo, and Naoki Kawashima

Comp. Phys. Commun. 217 (2017) 180-192.

in publications that include results obtained using this software.

Contents

• 1. Tutorial for calculations at zero temperature
  • 1.1. Spin 1/2 Dimer
    • 1.1.1. Check the energy
    • 1.1.2. Check S dependence
    • 1.1.3. Add magnetic field H
    • 1.1.4. Try to use Lanczos method
    • 1.1.5. Try to use LOBCG method
  • 1.2. Hubbard Dimer
    • 1.2.1. Check the energy
    • 1.2.2. Try to use LOBCG method
  • 1.3. Hubbard Trimer
    • 1.3.1. Ferromagnetic ground state
    • 1.3.2. Effects of transfer integrals
  • 1.4. Heisenberg chain (zero temperature)
    • 1.4.1. Check the energy
    • 1.4.2. Obtaining the excited state
    • 1.4.3. Size dependence of the spin gap
    • 1.4.4. Haldane gap
  • 1.5. J1-J2 Heisenberg model
    • 1.5.1. Calculations of spin structure factors for ground state
    • 1.5.2. Calculations of spin structure factors for excited states
  • 1.6. How to use Expert mode
    • 1.6.1. Exercise
  • 1.7. Use eigenvectors
    • 1.7.1. Exercise
• 2. Tutorial for finite-temperature calculations
  • 2.1. Heisenberg chain (finite temperatures)
    • 2.1.1. Full diagonalization
    • 2.1.2. Micro-canonical TPQ (mTPQ) method (Sz=0)
    • 2.1.3. mTPQ method (susceptibility)
    • 2.1.4. Canonical TPQ (cTPQ) method (Advanced)
  • 2.2. Kitaev cluster (finite temperatures)
    • 2.2.1. Lattice structure and eigen states of the Kitaev cluster
    • 2.2.2. Convergence of the microcanonical TPQ
• 3. Tutorials for real-time evolution
  • 3.1. U quench in Hubbard model
    • 3.1.1. Check norm and energy
    • 3.1.2. Dynamics of double occupation
  • 3.2. Dynamical phase transition in 1D transverse-field Ising model
    • 3.2.1. Ground state
    • 3.2.2. \(\Gamma\) quench
• 4. Tutorial for calculations of dynamical properties
  • 4.1. Dynamical spin structure factor
  • 4.2. Hubbard chain (optical conductivity)
  • 4.3. Spectrum calculation for 12-site one-dimeinsional Heisenberg chain model.