Document Type

Article

Publication Date

March 2013

Publication Title

Computer Physics Communications

Volume

184

Issue Number

3

First Page

557

Last Page

564

DOI

10.1016/j.cpc.2012.10.008

Keywords

Cluster, Expansions, Physics, Computer, Spin systems, Lattice models, hamiltonians, Accelerate, Thermodynamic, symmetries

Disciplines

Astrophysics and Astronomy | Physical Sciences and Mathematics | Physics

Abstract

We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques that can be used to accelerate the convergence of the series.

Comments

This is the Preprint of an article that was published in Computer Physics Communications, volume 184, issue 3, 2013. The Version of Record can be found online at this link.
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