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| documentation:language_reference:objects:responsefunction:functions:totightbinding [2024/12/23 18:02] – Maurits W. Haverkort | documentation:language_reference:objects:responsefunction:functions:totightbinding [2025/11/20 04:20] (current) – external edit 127.0.0.1 |
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| ====== ToTightbinding ====== | ====== ToTightBinding ====== |
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| 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. | 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. |
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| In the figure above (from [[https://doi.org/10.1103/PhysRevB.90.085102|PRB 90, 085102]]) we show the different tight binding layouts corresponding to the different response function representations. Panel (a) for tridiagonal, panel (b) for Anderson and panel (c) 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 [[documentation:language_reference:objects:responsefunction:functions:changetype|ResponseFunction.ChangeType()]]. | In the figure above (from [[https://doi.org/10.1103/PhysRevB.90.085102|PRB 90, 085102]]) we show the different tight binding layouts corresponding to the different response function representations. Panel (a) for Anderson, panel (b) for tridiagonal and panel %%(c)%% 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 [[documentation:language_reference:objects:responsefunction:functions:changetype|ResponseFunction.ChangeType()]]. |
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