Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder

TL;DR

This review explores the ground-state properties of the s=1/2 Heisenberg antiferromagnet on various two-dimensional lattices, highlighting the effects of lattice topology and quantum fluctuations on magnetic order and disorder.

Contribution

It provides a comprehensive summary of all 11 uniform Archimedean lattices, identifying conditions for semi-classical order and quantum disordered states, including the kagome and star lattices.

Findings

Most lattices exhibit semi-classical long-range order.

The kagome and star lattices show quantum disordered ground states.

Bond modifications induce quantum phase transitions.

Abstract

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.