Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries

TL;DR

This paper enhances the exact diagonalization method for quantum Heisenberg spin systems by integrating irreducible tensor operators with general point-group symmetries, enabling both exact and approximate energy eigenvalue calculations.

Contribution

It introduces a novel approach combining tensor operators and point-group symmetries to extend the applicability of exact diagonalization in quantum spin systems.

Findings

Successfully integrates tensor operators with point-group symmetries for exact diagonalization.

Proposes methods for approximate spectra using combined symmetries.

Improves computational efficiency in analyzing antiferromagnetic molecules.

Abstract

Numerical exact diagonalization is the ultimate method of choice in order to discuss static, dynamic, and thermodynamic properties of quantum systems. In this article we consider Heisenberg spin-systems and extend the range of applicability of the exact diagonalization method by showing how the irreducible tensor operator technique can be combined with an unrestricted use of general point-group symmetries. We also present ideas how to use spin-rotational and point-group symmetries in order to obtain approximate spectra.