Quantum Disordered Ground States in Frustrated Antiferromagnets with Multiple Ring Exchange Interactions

TL;DR

This paper identifies specific two-dimensional frustrated quantum spin systems with multiple ring exchange interactions that have quantum disordered ground states, including resonating valence bond and valence bond crystal states, related to quantum dimer models.

Contribution

It rigorously demonstrates the existence of quantum disordered ground states in certain frustrated antiferromagnets with ring exchange interactions, expanding understanding of quantum spin liquids.

Findings

Ground states are quantum disordered without magnetic long-range order.

Identifies conditions for resonating valence bond and valence bond crystal states.

Connects these systems to quantum dimer models.

Abstract

We present a certain class of two-dimensional frustrated quantum Heisenberg spin systems with multiple ring exchange interactions which are rigorously demonstrated to have quantum disordered ground states without magnetic long-range order. The systems considered in this paper are s=1/2 antiferromagnets on a honeycomb and square lattices, and an s=1 antiferromagnet on a triangular lattice. We find that for a particular set of parameter values, the ground state is a short-range resonating valence bond state or a valence bond crystal state. It is shown that these systems are closely related to the quantum dimer model introduced by Rokhsar and Kivelson as an effective low-energy theory for valence bond states.