Calculate NRG: Spectral Function for Anderson Model

[gonadas91]

Hi there! I've recently performed and NRG code to study one impurity model, related to the Anderson model. I want to calculate the density of states (spectral function) but I don't know if I am doing things right.

Since after some iterations we need to truncate the number of eigenstates of the hamiltonian, these are the only ones contributing to the next iteration. Since the hopping parameters of the Wilson chain decay exponentially, at each iteration there is a characteristic frecuency (omega) of the order of the hopping parameter for that Nth step.

My question is, when evaluating the density of states (on the impurity), we have the formula for T=0 of the matrix elements of the impurity operator, multiplied by Dirac delta functions. So each peak is multiplied by a "weight" given for that matrix elements squared. I am passing these delta functions to gaussian functions, whose width is of the order of the characteristic frecuency, but for each eigenstate, only evaluating these gaussians at w = 2wN, being wN the characteristic frecuency, is that alright¿ Thanks in advance

 

[eljose79]

Hello,

Thank you for sharing your experience with the NRG code and your question about calculating the density of states. Based on your description, it seems like you are on the right track in your approach.

When evaluating the density of states, it is important to take into account the truncation of eigenstates and the characteristic frequency of the hopping parameters. The use of Gaussian functions with a width of the order of the characteristic frequency is a common approach in NRG calculations. However, it is important to make sure that the Gaussians are centered at the correct frequency for each eigenstate, as you have mentioned. It is also important to consider the energy resolution and the number of eigenstates used in the calculation to ensure accurate results.

In addition to the technical aspects, it is also important to carefully analyze and interpret the results of the density of states calculation. This can provide valuable insights into the behavior of the system and can help validate the accuracy of the NRG code.

Overall, it seems like you are taking the necessary steps in your calculation. I would suggest double-checking the centering of the Gaussians and the energy resolution used, and also carefully analyzing the results to ensure their accuracy. If you have any further questions, please don't hesitate to reach out for assistance.

Best of luck with your research!