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

TL;DR

QS$^{3}$ is a computational package that efficiently analyzes large-scale quantum spin systems near saturation, utilizing symmetry-adapted bases and Lanczos methods to handle systems with over 1000 sites.

Contribution

The paper introduces QS$^{3}$, a novel software that performs large-scale quantum spin calculations without bit representations, enabling analysis of systems with over 1000 sites near saturation.

Findings

Successfully benchmarked on 10x10x10 cubic lattice.

Achieved efficient parallelization on supercomputers.

Accurately computed spin structure factors and excitation spectra.

Abstract

We develop a program package named QS$^{3}$ [\textipa{kj\'u:-\'es-kj\'u: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 $\boldsymbol{k}$ 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 $10\times10\times10$ cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the $10\times10$ 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.