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documentation:language_reference:objects:responsefunction:functions:calculatehybridizationfunction [2024/12/23 23:56] – Maurits W. Haverkortdocumentation:language_reference:objects:responsefunction:functions:calculatehybridizationfunction [2024/12/24 00:19] (current) – Maurits W. Haverkort
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 ### ###
-Responsefunction.CalculateHybridizationFunction(G0,Sigma) calculates the interacting impurity bath Green's function. Given a lattice with local Green's function $G_0(\omega)$ and a local self energy $\Sigma(\omega)$. The full Green's function then is $G(\omega) = G_0(\omega-\Sigma(\omega))$. If we want to add a self energy on all sites, except for the site we are looking at we get $$G_{Bath} = \frac{1}{G_0(\omega-\Sigma(\omega))^{-1} - \Sigma(\omega)}$$. This Green's function can be used to define the hybridisation function of an Anderson impurity model representing a lattice. +Responsefunction.CalculateHybridizationFunction(G0,Sigma) calculates the interacting impurity bath Green's function. Given a lattice with local Green's function $G_0(\omega)$ and a local self energy $\Sigma(\omega)$. The full Green's function then is $G(\omega) = G_0(\omega-\Sigma(\omega))$. If we want to add a self energy on all sites, except for the site we are looking at we get $$G_{Bath} = \frac{1}{G_0(\omega-\Sigma(\omega))^{-1} - \Sigma(\omega)}$$ This Green's function can be used to define the hybridisation function of an Anderson impurity model representing a lattice. This is useful for the DMFT approximation where we define a lattice model with local interactions on all lattice sites. We replace the interactions on all sites but one by a local self energy. 
 ### ###
  
 ===== Input ===== ===== Input =====
 +
 +  - $G_0$ the one particle Green's function for the non-interacting lattice. Given in one of the available response function formats. 
 +  - $\Sigma$ the local self energy. Given in one of the available response function formats. 
 +  - A list of options. Available are
 +  *    EnergyGrid - a table of discrete energies used for the possible values of the Bath energies for a representation of $G_{Bath}(\omega)$ in Anderson matrix format.
  
 ===== Output ===== ===== Output =====
 +
 +  - A response function representing $G_{Bath}(\omega)$.
  
 ===== Example ===== ===== Example =====
  
 ### ###
-description text+The example below uses some arbitrary definition for $G_0$ and $\Sigma$. Examples where these functions are used can be found in the tutorials.
 ### ###
  
 ==== Input ==== ==== Input ====
 <code Quanty Example.Quanty> <code Quanty Example.Quanty>
--- some example code+a = {0, 0, -2,0,2} 
 +b = {   1,  1,1,1} 
 +G0 = ResponseFunction.New( { a, b, mu=0, type="And", name="G0"} ) 
 + 
 +a = {0,0,0,0} 
 +b = {0.1,0.1,0.1} 
 +Sigma = ResponseFunction.New( { a, b, mu=0, type="Tri", name="Sigma"} ) 
 + 
 +GHyb = ResponseFunction.CalculateHybridizationFunction(G0,Sigma) 
 + 
 +print("The non interacting Green's function") 
 +print(G0) 
 +print("The self energy") 
 +print(Sigma) 
 +print("The bath Green's function defining the hybridization function for the full interacting bath") 
 +print(GHyb)
 </code> </code>
  
 ==== Result ==== ==== Result ====
 <file Quanty_Output> <file Quanty_Output>
-text produced as output+The non interacting Green's function 
 +{ { 0 , 0 , -2 , 0 , 2 } ,  
 +  { 1 , 1 , 1 , 1 } , 
 +  name = G0 , 
 +  mu = 0 , 
 +  type = And } 
 +The self energy 
 +{ { 0 , 0 , 0 , 0 } ,  
 +  { 0.1 , 0.1 , 0.1 } , 
 +  name = Sigma , 
 +  mu = 0 , 
 +  type = Tri } 
 +The bath Green's function defining the hybridization function for the full interacting bath 
 +{ { 0 , 0 , -2.0049999999223 , -0.16180339887499 , -0.14261254104408 , -0.14010864678943 , -0.061803398874989 , -0.0024961056676115 , 0.0024961056676115 , 0.061803398874989 , 0.14010864678943 , 0.14261254104408 , 0.16180339887499 , 2.0049999999223 } ,  
 +  { 1 , 0.99874921790792 , 0.37174803446018 , 0.0238150684481 , 0.026242558358305 , 0.60150095500755 , 0.03527279934937 , 0.03527279934937 , 0.60150095500755 , 0.026242558358305 , 0.0238150684481 , 0.37174803446018 , 0.99874921790792 } , 
 +  name = GBath , 
 +  mu = 0 , 
 +  type = And }
 </file> </file>
  

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