spectral_function

tenpy.tools.spectral_function_tools.spectral_function(time_dep_corr, lat, dt: float, gaussian_window: bool = False, sigma: float = 0.4, linear_predict: bool = False, rel_prediction_time: float = 1, rel_num_points: float = 0.3, truncation_mode: str = 'renormalize', rel_split: float = 0, axis_time: int = 0, axis_space: int = 1)[source]

Given a time dependent correlation function C(t, r), calculate its Spectral Function.

After a run of TimeDependentCorrelation, a DataLoader instance should be passed, from which the underlying lattice and additional parameters (e.g. dt) can be extracted. The correlation_key must coincide with the key of the time-dep. correlation function in the output of the Simulation.

Parameters:

  • time_dep_corr (np.ndarray) – Time dependent correlation :math`C(t, r)`

  • lat (Lattice) – instance of a lattice

  • dt (float) – time-step discretization of the t_dep_correlation

  • gaussian_window (bool) – boolean flag to apply gaussian windowing

  • sigma (float) – standard-deviation used for the gaussian window

  • linear_predict (bool) – boolean flag to apply linear prediction

  • rel_prediction_time (float) – relative time to predict, defaults to 1

  • rel_num_points (float) – relative percentage of last points to base linear prediction on

  • truncation_mode (str) – truncation_mode of get_alpha_and_c()

  • rel_split (float) – percentage of the data to be discarded during training

  • axis_time – time axis (default 0)

  • axis_space – axis of mps tensors (default 1)

Returns:

dictionary of keys for k, k_reduced, w and for the spectral function S

Return type:

dict

Notes

The Spectral Function is given by the fourier transform in space and time of the (time-dep.) correlation function. For a e.g. translationally invariant system, this is .. math

S(w, \mathbf{k}) = \int dt e^{-iwt} \int d\mathbf{r} e^{i \mathbf{k} \mathbf{r} C(t, \mathbf{r})