Variational Hilbert space truncation approach to quantum Heisenberg antiferromagnets on frustrated clusters

TL;DR

This paper introduces a variational Hilbert space truncation method to accurately study the ground states of frustrated quantum Heisenberg antiferromagnets on finite clusters, overcoming limitations of traditional computational approaches.

Contribution

The authors develop an efficient variational truncation technique for exact diagonalization, enabling analysis of larger frustrated clusters without symmetry restrictions.

Findings

Accurate ground state energies for clusters up to 32 sites.

Effective spin-spin correlation calculations in frustrated geometries.

Comparison shows improved results over full-space calculations and unfrustrated structures.

Abstract

We study the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a series of finite-size clusters with features inspired by the fullerenes. Frustration due to the presence of pentagonal rings makes such structures challenging in the context of quantum Monte-Carlo methods. We use an exact diagonalization approach combined with a truncation method in which only the most important basis states of the Hilbert space are retained. We describe an efficient variational method for finding an optimal truncation of a given size which minimizes the error in the ground state energy. Ground state energies and spin-spin correlations are obtained for clusters with up to thirty-two sites without the need to restrict the symmetry of the structures. The results are compared to full-space calculations and to unfrustrated structures based on the honeycomb lattice.