Extension of the Lieb-Schupp theorem to the Heisenberg models with higher order interactions

TL;DR

This paper extends the Lieb-Schupp theorem to Heisenberg models with higher order interactions on various lattices, demonstrating that all ground states have total spin zero in a broad parameter range beyond previous Marshall-Lieb-Mattis results.

Contribution

The authors generalize the Lieb-Schupp theorem to include higher order interactions on complex lattices with reflection symmetry, expanding the understanding of ground state properties.

Findings

All ground states have total spin zero in the extended models.

The results apply to both frustrated and non-frustrated lattices with reflection symmetry.

The theorem covers a wider interaction parameter region than previous results.

Abstract

We extend the Lieb-Schupp theorem to the Heisenberg models with higher order interactions on non-frustrated or frustrated finite lattices. These lattices are constructed by even numbered rings with or without crossing bonds and have reflection symmetry. The results show that all ground states have total spin zero in wide interaction parameters region which is not covered with the results of the Marshall-Lieb-Mattis type arguments.