Coupled Cluster Treatment of the XY model

TL;DR

This paper applies the coupled-cluster method to analyze quantum XY spin models across 1D, 2D, and 3D lattices, providing accurate ground-state and excitation energies as functions of anisotropy.

Contribution

It extends the coupled-cluster method to higher-dimensional XY models and compares results with exact and numerical methods, demonstrating its effectiveness.

Findings

Critical points near $oldsymbol{ ext{γ=0}}$ are accurately identified.

Ground-state energy results are well converged except near critical points.

The method provides reliable estimates for various lattice dimensions.

Abstract

We study quantum spin systems in the 1D, 2D square and 3D cubic lattices with nearest-neighbour XY exchange. We use the coupled-cluster method (CCM) to calculate the ground-state energy, the T=0 sublattice magnetisation and the excited state energies, all as functions of the anisotropy parameter $\gamma$. We consider $S=1/2$ in detail and give some results for higher $S$. In 1D these results are compared with the exact $S=1/2$ results and in 2D with Monte-Carlo and series expansions. We obtain critical points close to the expected value $\gamma=0$ and our extrapolated LSUBn results for the ground-state energy are well converged for all $\gamma$ except very close to the critical point.