Combined use of translational and spin-rotational invariance for spin systems

Abstract

Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing computational effort is to take advantage of the translational symmetry $C_N$ in periodic systems. This represents a rather simple yet elegant application of the group theoretical symmetry projection operator technique. For isotropic exchange interactions, the spin-rotational symmetry SU(2) can be used, where the Hamiltonian matrix is block-structured according to the total spin- and magnetization quantum numbers. Rewriting the Heisenberg Hamiltonian in terms of irreducible tensor operators allows for an efficient and highly parallelizable implementation to calculate its matrix elements recursively in the spin-coupling basis. When combining both $C_N$ and SU(2), mathematically, the symmetry projection technique leads to ready-to-use formulas. However, the evaluation of these formulas is very demanding in both computation time and memory consumption, problems which are said to outweigh the benefits of the symmetry reduced matrix shape. We show a way to minimize the computational effort for selected systems and present the largest numerically accessible cases.

7 pages, 5 figures

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• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
• Magneto- and barocaloric properties of the ferro-antiferromagnetic sawtooth chain
• Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach
• Analytical solutions of symmetric isotropic spin clusters
• Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters
• Thermal DMRG for highly frustrated quantum spin chains: a user perspective
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth
• Quantum Entanglement Generation in the Heterometallic Ni${}_4^{\text{2+}}$Gd${}_4^{\text{3+}}$ Complexes