Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 184, Issue 3, Pages 557-564Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2012.10.008
Keywords
Linked-cluster expansions; Exact diagonalization; Spin systems; Lattice models
Funding
- National Science Foundation (NSF) [OCI-0904597]
- NSF
- Kraken at the National Institute for Computational Science [TG-DMR100026]
- Office of Advanced Cyberinfrastructure (OAC)
- Direct For Computer & Info Scie & Enginr [0904597] Funding Source: National Science Foundation
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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. (C) 2012 Elsevier B.V. All rights reserved.
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