Some properties of frustrated spin systems: extensions and applications of Lieb-Schupp approach

TL;DR

This paper extends Lieb-Schupp's spin-reflection positivity method to prove ground-state properties of frustrated Heisenberg models under various symmetries and applies these results to multidimensional lattice systems.

Contribution

It generalizes the Lieb-Schupp approach to include symmetries beyond reflection, such as inversion, and applies the results to complex multidimensional lattice models.

Findings

Ground state is a singlet under broader symmetry conditions.

Relations between ground-state energies are established for various lattice models.

Method extends applicability to multidimensional frustrated spin systems.

Abstract

Lieb and Schupp have obtained, using certain version of ``spin-reflection positivity'' method, a number of ground-state properties for frustrated Heisenberg models. One group of these results is related to singlet nature of ground state and it needs an assumption of reflection symmetry present in the system. In this paper, it is shown that the result holds also for other symmetries (inversion etc.). The second Lieb-Schupp result is relation between ground-state energies of certain systems. In the paper, this relation is applied to multidimensional models on various lattices.