A short introduction to numerical linked-cluster expansions

Baoming Tang, Ehsan Khatami, Marcos Rigol

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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.

Original languageEnglish (US)
Pages (from-to)557-564
Number of pages8
JournalComputer Physics Communications
Volume184
Issue number3
DOIs
StatePublished - Mar 1 2013

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All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • Physics and Astronomy(all)

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