Quantum lattice model solver HΦ

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

61 Citations (Scopus)


HΦ [aitch-phi] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, HΦ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, HΦ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of HΦ. We also show the benchmark results of HΦ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP). Program summary Program Title:HΦ Program Files doi: http://dx.doi.org/10.17632/vnfthtyctm.1 Licensing provisions: GNU General Public License, version 3 or later Programming language: C External routines/libraries: MPI, BLAS, LAPACK Nature of problem: Physical properties (such as the magnetic moment, the specific heat, the spin susceptibility) of strongly correlated electrons at zero- and finite-temperature. Solution method: Application software based on the full diagonalization method, the exact diagonalization using the Lanczos method, and the microcanonical thermal pure quantum state for quantum lattice model such as the Hubbard model, the Heisenberg model and the Kondo model. Restrictions: System size less than about 20 sites for an itinerant electronic system and 40 site for a local spin system. Unusual features: Finite-temperature calculation of the strongly correlated electronic system based on the iterative scheme to construct the thermal pure quantum state. This method is efficient for highly frustrated system which is difficult to treat with other methods such as the unbiased quantum Monte Carlo.

Original languageEnglish
Pages (from-to)180-192
Number of pages13
JournalComputer Physics Communications
Publication statusPublished - 2017 Aug


  • Lattice fermion models
  • Numerical linear algebra
  • Quantum spin liquids

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)


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