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.

arXiv comment15 pages, 4 figures, Source codes are available at https://github.com/QS-Cube/ED

References in corpus (30)

• Correlated Electrons in High Temperature Superconductors
• The ALPS project release 1.3: open source software for strongly correlated systems
• Computational Studies of Quantum Spin Systems
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Nematic order in square lattice frustrated ferromagnets
• Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
• Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field
• Pushing Configuration-Interaction to the Limit: Towards Massively Parallel MCSCF Calculations
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Multi-magnon bound states in the frustrated ferromagnetic 1D chain
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Correlation functions and excitation spectrum of the frustrated ferromagnetic spin-1/2 chain in an external magnetic field
• Static and dynamical spin correlations of the S=1/2 random-bond antiferromagnetic Heisenberg model on the triangular and the kagome lattices
• Quantum Lattice Model Solver $\mathcal{H}\Phi$
• The phase diagram of the antiferromagnetic XXZ model on the triangular lattice
• Spin-Nematic and Spin-Density-Wave Orders in Spatially Anisotropic Frustrated Magnets in a Magnetic Field
• A Comparative Study of the Magnetization Process of Two-Dimensional Antiferromagnets
• Quantum spin-liquid behavior in the spin-1/2 random-bond Heisenberg antiferromagnet on the kagome lattice
• Magnetocaloric effect in the frustrated square lattice J1-J2 model
• Magnon BEC and various phases of 3D quantum helimagnets under high magnetic field
• Randomness-induced quantum spin liquid behavior in the $s=\frac{1}{2}$ random $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice
• Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
• Randomness-induced quantum spin liquid behavior in the s=1/2 random J1-J2 Heisenberg antiferromagnet on the honeycomb lattice
• Randomness-induced quantum spin liquid behavior in the $s=$1/2 bond-random Heisenberg antiferromagnet on the pyrochlore lattice
• Nematic phase and phase separation near saturation field in frustrated ferromagnets
• Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation
• Magnetic phase diagram slightly below the saturation field in the stacked $J_1$-$J_2$ model in the square lattice with the $J_{\text{C}}$ interlayer coupling

Cited by in corpus (2)

• Update of $\mathcal{H}\Phi$: Newly added functions and methods in versions 2 and 3
• Dynamics of Interacting Bosons on the Sawtooth Lattice with a Flat Band