ResponseFunction.ToTightbinding(G) transforms a response function object to a tight binding object that, when solved, has the response function $G$ as its one particle Green's function.

Depending on the representation used for the response function (Tridiagonal, Anderson, or Natural impurity orbitals) one finds a different layout of the tight binding Hamiltonian that it represents. Transformations between the different layouts are given by unitary basis transformations. In all cases the dimension of the sites, i.e. the number of quantum degrees of freedom per site such as spin-orbitals, is given by the BlockSize of the response function. The tridiagonal representation of the response function maps to a tight binding model of a one dimensional chain. The Anderson representation of the response function maps to a single impurity interacting with many bath sites that do not interact with each other. The natural impurity representation maps to an impurity that interacts with a single bath site (the extended bath site). The impurity and extended bath then interact both with two separate chains of bath states, one related to the valence bath and one to the conduction bath.

In the figure above we show the different tight binding layouts corresponding to the different response function representations. Panel (a) for tridiagonal, panel (b) for Anderson and panel © for natural impurity. The square sites refer to the impurity, the circular to the bath sites. Each site can represent a number of spin-orbitals depending on the BlockSize of the response function. The lines represent hopping matrix elements. The red colour for the different sites refers to the approximate filling of the sites. The tridiagonal representation is nice as each site only interacts with one other site, however it does mean that all sites are partially filled. The Anderson representation is nice as the bath sites do not interact and the bath sites with low (high) energy are larger filled (empty). The natural impurity orbital representation has one bath site that is partially filled, all others are either completely empty or completely filled. Note that chaining between representation is given by a unitary transformation, which can by done by the function ResponseFunction.ChangeType().

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Example.Quanty

-- some example code

text produced as output