High-Order Coupled Cluster Method Calculations using Three-Dimensional Model States: An Illustration for the Triangular-Lattice Antiferromagnet in an External Field

TL;DR

This paper extends the coupled cluster method (CCM) to include three-dimensional non-coplanar model states, enabling analysis of complex quantum spin systems like the triangular-lattice antiferromagnet in a magnetic field.

Contribution

It introduces a novel approach for applying CCM with 3D model states, allowing for the treatment of complex Hamiltonians and providing new insights into frustrated quantum spin systems.

Findings

Coplanar states have lower energy than non-coplanar states across all fields.

The non-coplanar state does not reveal the spin plateau.

The approach validates the use of 3D model states in CCM calculations.

Abstract

The coupled cluster method (CCM) has previously been applied to study the ground- and excited-state properties of many different types of frustrated and unfrustrated quantum spin systems. A common feature in the application of the CCM is to rotate the local spin axes of the (often classical) model state so that (notationally only) the spins all appear to point in the downwards $z$-direction. Hitherto, we remark that only coplanar model states have been used because they do not lead to imaginary terms in the new Hamiltonian. By contrast, non-coplanar "three-dimensional" (3D) model states can lead to imaginary terms in the new Hamiltonian after rotation. In principle, however, macroscopic quantities predicted by the CCM (such as the ground-state energy and order parameter) should still be real (even though the Hamiltonian may be complex) because the transformations of local spin axes are unitary. Here we explain how we may use such 3D model states for the CCM and how we may solve for the (now possibly complex) CCM correlation coefficients. We present results for the spin-half triangular-lattice antiferromagnet in an external magnetic field. We use both coplanar model states and a single 3D non-coplanar model state. We calculate the ground-state energy and the lattice magnetisation as a function of the magnetic field strength. We find that the energies of the coplanar states lie lower than that of the non-coplanar state for all values of the external field, as seen in other approximate studies for this model. We find that the non-coplanar state does not detect the well-known spin plateau occurring in this model, although (as seen before) it is clearly observed for the coplanar model states using the CCM. These results are an excellent initial validation of the new approach for the application of the CCM using 3D model states.