The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models

TL;DR

This paper introduces the LPSUB$m$ approximation scheme for the coupled cluster method, applied to quantum lattice models, providing accurate results for ground-state properties and critical points, and comparing it with existing schemes.

Contribution

The paper presents a novel LPSUB$m$ approximation scheme for CCM applicable to lattice systems, demonstrating its effectiveness on quantum spin models and comparing it with other established methods.

Findings

LPSUB$m$ scheme yields ground-state energies consistent with other methods.

Accurate sublattice magnetization and critical points obtained.

Each CCM scheme (LSUB$m$, DSUB$m$, LPSUB$m$) has unique advantages.

Abstract

A new approximation hierarchy, called the LPSUB$m$ scheme, is described for the coupled cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-1/2 Heisenberg antiferromagnetic) spin-lattice models, namely: the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods and the CCM using the alternative LSUB$m$ and DSUB$m$ schemes. Each of the three CCM schemes (LSUB$m$, DSUB$m$ and LPSUB$m$) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.