Linked-Cluster Series-Expansion Methods for Quantum Lattice Models

Rajiv SinghUniversity of California, Davis (UC Davis)

There are several computational approaches to Quantum Lattice Models that are based on the Linked-cluster theorem of statistical mechanics. The most well known of these is the method of high temperature series expansions, where thermodynamic properties of a Quantum Lattice Model are expressed as a Taylor series expansion in powers of $\beta=1/kT$. Expansion coefficients, for a wide range of models, can be computed by automated computer programs up to order 10 or higher, depending on the complexity of the model. Linked cluster expansions can also be used to develop coupling-constant series expansions for ground state properties and elementary excitation spectra of some Quantum Lattice Models. In our talk, we will discuss:

(i) Formalism of Linked Cluster Methods;
(ii) Calculation of series expansion coefficients on a computer;
(iii) Physical quantities that can be calculated by these methods:
(iv) Range of models whose properties can be addressed by these methods;
(v) Series extrapolation methods and critical phenomena;
(vi) Relationship of series expansion methods to other computational methods.

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