Divide and conquer the Hilbert space of translation-symmetric spin systems

Abstract

Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the "sublattice coding" of H. Q. Lin. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond 10^11 become accessible.

9 pages

References in corpus (6)

• The Kernel Polynomial Method
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Short-distance thermal correlations in the XXZ chain
• On the absorption of microwaves by the one-dimensional spin-1/2 Heisenberg-Ising magnet
• On the theory of microwave absorption by the spin-1/2 Heisenberg-Ising magnet

Cited by in corpus (6)

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• Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state
• Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice
• Anisotropic magnetic interactions and spin dynamics in the spin-chain compound Cu(py)${}_2$Br${}_2$: An experimental and theoretical study
• DanceQ: High-performance library for number-conserving bases