Numerical linked-cluster algorithms. I. Spin systems on square, triangular, and kagomé lattices

2007/06/21 by Marcos Rigol, Tyler Bryant, Rajiv R. P. Singh · 2 citations
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physreve.75.061118

published as Phys. Rev. E 75, 061118 (2007) · 14 pages, 16 figures, as published

openalex publication_date 2007/06/21 · arxiv created 2007/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 kagomé lattices. Results for several choices of clusters and extrapolations methods, that accelerate the convergence of NLCs, 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.

Citations

• Low Temperature Behavior and Crossovers of the Square Lattice Quantum Heisenberg Antiferromagnet
• A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

Cited by

• Numerical linked-cluster algorithms. II.t−Jmodels on the square lattice
• Finite-temperature spin dynamics and phase transitions in spin-orbital models