Quantum spin solver near saturation: QS3

Abstract

We develop a program package named QS3▪ based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type quantum spin models on spatially uniform/non-uniform lattices near fully polarized states, which can be mapped to dilute hardcore Bose systems. All calculations in QS3, including eigenvalue problems, expectation values for one/two-point spin operators, and static/dynamical spin structure factors, are performed in the symmetry-adapted bases specified by the number N↓ of down spins and the wave number k associated with the translational symmetry without using the bit representation for specifying spin configurations. Because of these treatments, QS3 can support large-scale quantum systems containing more than 1000 sites with dilute N↓. We show the benchmark results of QS3 for the low-energy excitation dispersion of the isotropic Heisenberg model on the 10×10×10 cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the 10×10 square lattice, and the open-MP parallelization efficiency on the supercomputer (Ohtaka) based on AMD Epyc 7702 installed at the Institute for the Solid State Physics (ISSP). Theoretical backgrounds and the user interface of QS3 are also described. Program summaryProgram Title: QS3CPC Library link to program files:https://doi.org/10.17632/yc6jytvf8v.1Developer's repository link:https://github.com/QS-Cube/EDLicensing provisions: MITProgramming language: Fortran90External routines/libraries: BLAS, LAPACKNature of problem: Physical properties (such as total energy, magnetic moment, two-point spin correlation function, and dynamical structure factor)Solution method: Application software based on the full diagonalization method and the exact diagonalization method using the Lanczos and thick-restart Lanczos techniques for quantum spin S=1/2 models such as the XXZ model.Restrictions: Spin S=1/2 systems with U(1) symmetry.Unusual features: Massively large quantum spin systems with U(1) symmetry near the saturation field can be solved with or without considering translational symmetry, which is difficult to treat using standard exact diagonalization libraries with the bit representation for specifying spin configurations.