Coupled-cluster method: A lattice-path-based subsystem approximation scheme for quantum lattice models

An approximation hierarchy, called the lattice-path-based subsystem (LPSUB$m$) approximation 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-$\frac{1}{2}$ Heisenberg antiferromagnetic) spin-lattice models, namely, the $\mathit{XXZ}$ and the $\mathit{XY}$ 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 lattice-animal-based subsystem (LSUB$m$) and the distance-based subsystem (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.

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