Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices

TL;DR

This paper introduces numerical linked-cluster (NLC) algorithms for calculating temperature-dependent properties of quantum spin systems on various lattices, demonstrating improved accuracy over traditional methods like high-temperature expansions and exact diagonalization.

Contribution

The paper presents the application of NLC algorithms to spin models on square, triangular, and kagome lattices, including convergence acceleration techniques and comparative analysis with other methods.

Findings

NLC results outperform HTE and ED in accuracy for many models.

NLC effectively computes thermodynamic properties in the thermodynamic limit.

Comparison shows NLC's advantages over other computational approaches.

Abstract

We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We present studies of thermodynamic observables for spin models on square, triangular, and kagome lattices. Results for several choices of clusters and extrapolations methods, that accelerate the convergence of NLC, are presented. We also include a comparison of NLC results with those obtained from exact analytical expressions (where available), high-temperature expansions (HTE), exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo simulations.For many models and properties NLC results are substantially more accurate than HTE and ED.