Quantum spin solver near saturation: QS${}_{}^3$

Abstract

We develop a program package named QS${}^3$ [\textipa{kjú:-és-kjú:b}] 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 QS${}^3$, 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 $N_{\downarrow }$ of down spins and the wave number $\mathbf{k}$ associated with the translational symmetry without using the bit representation for specifying spin configurations. Because of these treatments, QS${}^3$ can support large-scale quantum systems containing more than 1000 sites with dilute $N_{\downarrow }$. We show the benchmark results of QS${}^3$ for the low-energy excitation dispersion of the isotropic Heisenberg model on the $10\times 10\times 10$ cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the $10\times 10$ 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 QS${}^3$ are also described.

15 pages, 4 figures, Source codes are available at https://github.com/QS-Cube/ED

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