Symmetry considerations in exact diagonalization: spin-1/2 pyrochlore magnets

TL;DR

This paper demonstrates how group theory symmetries can be used to optimize the exact diagonalization of a 16-site spin-1/2 pyrochlore lattice, enabling more efficient quantum system analysis.

Contribution

It introduces a method to analytically construct symmetrized states for block-diagonalizing the Hamiltonian in pyrochlore lattice systems.

Findings

Complete set of symmetrized states constructed

Hamiltonian block-diagonalized using symmetry considerations

Enhanced efficiency in exact diagonalization of quantum systems

Abstract

We describe how the methods of group theory (symmetry) are used to optimize the problem of exact diagonalization of a quantum system on a 16-site pyrochlore lattice. By analytically constructing a complete set of symmetrized states, we completely block-diagonalize the Hamiltonian. As an example, we consider a spin-1/2 system with nearest neighbour exchange interactions.