TY - JOUR
T1 - A short introduction to numerical linked-cluster expansions
AU - Tang, Baoming
AU - Khatami, Ehsan
AU - Rigol, Marcos
N1 - Funding Information:
This research was supported by the National Science Foundation (NSF) under Grant No. OCI-0904597 and enabled by an allocation of advanced computing resources, supported by the NSF. The computations in Section 3 were performed on Kraken at the National Institute for Computational Science under Account No. TG-DMR100026.
PY - 2013/3
Y1 - 2013/3
N2 - 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.
AB - 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.
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U2 - 10.1016/j.cpc.2012.10.008
DO - 10.1016/j.cpc.2012.10.008
M3 - Article
AN - SCOPUS:84872028074
SN - 0010-4655
VL - 184
SP - 557
EP - 564
JO - Computer Physics Communications
JF - Computer Physics Communications
IS - 3
ER -