Introduction to HΦ

An exact diagonalization package for a wide range of quantum lattice models (e.g. multi-orbital Hubbard model, Heisenberg model, Kondo lattice model). HΦ also supports the massively parallel computations. The Lanczos algorithm for obtaining the ground state and thermal pure quantum state method for finite-temperature calculations are implemented. In addition, dynamical Green’s functions can be calculated using Kω, which is a library of the shifted Krylov subspace method. It is possible to perform simulations for real-time evolution from ver. 3.0.

Availability

The supercomputer system-B “sekirei” and system-C “enaga” in ISSP
Linux PC + intel compiler, Linux PC + gcc, Mac + gcc, Mac + intel compiler

Target substance/model

Hubbard model, Heisenberg model, Kondo lattice model, Kitaev model, Kitaev-Heisenberg model, multi-orbital Hubbard model

Physical quantities that can be computed

specific heat, susceptibility, ground state energy, free energy, structure factors

Methodology

Lanczos algorithm, thermal pure quantum state, conjugate gradient method, full diagonalization

Parallelization

MPI/OpenMP hybrid parallelization is supported.
GPGPU is available in full diagonalization method (from ver. 3.1).

Core Developers

  • Youhei Yamaji (Quantum-Phase Electronics Center, The University of Tokyo)
  • Takahiro Misawa (Institute for Solid State Physics, The University of Tokyo)
  • Kazuyoshi Yoshimi (Institute for Solid State Physics, The University of Tokyo)
  • Mitsuaki Kawamura (Institute for Solid State Physics, The University of Tokyo),
  • Yuichi Motoyama (Institute for Solid State Physics, The University of Tokyo)
  • Kota Ido (Institute for Solid State Physics, The University of Tokyo)
  • Synge Todo (Department of Physics, The University of Tokyo)
  • Naoki Kawashima (Institute for Solid State Physics, The University of Tokyo)

License

GNU GPL version 3
This software is developed under the support of “Project for advancement of software usability in materials science” by The Institute for Solid State Physics, The University of Tokyo. We hope that you cite the following reference when you publish the results using HΦ (hphi):

“Quantum lattice model solver HΦ”, M. Kawamura, K. Yoshimi, T. Misawa, Y. Yamaji, S. Todo, and N. Kawashima, Computer Physics Communications 217, 180 (2017).

Bibtex:

@article{KAWAMURA2017180,
title = {Quantum lattice model solver HΦ},
journal = {Computer Physics Communications},
volume = {217},
pages = {180-192},
year = {2017},
issn = {0010-4655},
doi = {https://doi.org/10.1016/j.cpc.2017.04.006},
url = {https://www.sciencedirect.com/science/article/pii/S0010465517301200},
author = {Mitsuaki Kawamura and Kazuyoshi Yoshimi and Takahiro Misawa and Youhei Yamaji and Synge Todo and Naoki Kawashima}
}