dmft.plot.hf_single_site

Plotting utilities for the Single site DMFT phase diagram

Functions

dmft.plot.hf_single_site.autocorrelation_function(spins_log)

Calculates the autocorrelation function of the auxiliary Ising fields

Parameters:spins_log (ndarray 1D or 2D) – Monte Carlo time evolution of the auxiliary Ising field
Returns:
Return type:ndarray
dmft.plot.hf_single_site.averager(sim_dir, observable, last_iterations)

Averages the observable arrays in sim_dir for the last_iterations

last_iteration is a list of folder names

dmft.plot.hf_single_site.collect_bined_saves()
dmft.plot.hf_single_site.energies(beta, filestr='SB_PM_B{}.h5')

returns the potential, and kinetic energy

Parameters:
  • beta (float, inverse temperature) –
  • filestr (string, results file name, beta is replaced in format) –
Returns:

Contains, potential energy, Kinetic energy, values of U
Return type:

tuple of 3 ndarrays
dmft.plot.hf_single_site.fit_dos(beta, avg, filestr='disk/SB_PM_B{}')

Fits for all Green’s functions at a given beta their density of states at the Fermi energy

Parameters:
  • beta (float inverse temperature) –
  • avg (int number of last iterations to average over) –
Returns:
Return type:

arrays of Interaction, Fitted and source GF imaginary part
dmft.plot.hf_single_site.get_giw(sim_dir, iteration_slice, tau=None, w_n=None, setup=None)

Recovers with Fourier Transform G_iw from H5 file

Parameters:
  • h5parent (hdf5 group to go) –
  • iteration_slice (list of iteration names to average over) –
  • tau (1D real array time slices of HF data) –
  • w_n (1D real array matsubara frequencies) –
Returns:

tuple
Return type:

G(\tau), G(i\omega_n)
dmft.plot.hf_single_site.get_sigmaiw(h5parent, iteration, tau, w_n)

Returns the self-energy with the Dyson equation

dmft.plot.hf_single_site.gf_tail(gtau, U, mu)

Estimates the known first 3 moments of the tail

Starting from the high energy expansion of [self-energy]

\Sigma(i\omega_n \rightarrow \infty) = U \left(n_{\bar{\sigma}} - \frac{1}{2}\right) + \frac{U^2}{i\omega_n} n_{\bar{\sigma}} (1 - n_{\bar{\sigma}})

Then in the Bethe lattice where the self consistency is -t^2G the Green function decays as

G(i\omega_n \rightarrow \infty) = \frac{1}{i\omega_n} - \frac{\mu + U(\frac{1}{2} + G(\tau=0^+))}{(i\omega_n)^2} + \frac{t^2 + U^2/4 + \mu^2 - U\mu + 2U\mu G(\tau=0^+)}{(i\omega_n)^3}

Parameters:
  • gtau (Imaginary Time Green function array) –
  • U (float Local interaction) –
  • mu (float chemical potential) –
Returns:
Return type:

list

References

[self-energy]: Gull, E. et al. Reviews of Modern Physics, 83(2), 384 http://dx.doi.org/10.1103/RevModPhys.83.349
dmft.plot.hf_single_site.glob(pathname, *, recursive=False)

Return a list of paths matching a pathname pattern.

The pattern may contain simple shell-style wildcards a la fnmatch. However, unlike fnmatch, filenames starting with a dot are special cases that are not matched by ‘*’ and ‘?’ patterns.

If recursive is true, the pattern ‘**’ will match any files and zero or more directories and subdirectories.

dmft.plot.hf_single_site.interpol(gtau, Lrang, add_edge=False, same_particle=False)

This function interpolates G(\tau) onto a different array

it keep track of the shape of the Greens functions in Beta^-.

Parameters:
  • gtau (ndarray) – Green function to interpolate
  • Lrang (int) – number of points to describe
  • add_edge (bool) – if the point Beta^- is missing add it
  • same_particle (bool) – because fermion commutation relations if same fermion the edge has an extra -1
dmft.plot.hf_single_site.label_convergence(beta, u_int, axes, graf, n_freq, xlim)

Label the axes of the common plot of the evolution of DMFT loops

dmft.plot.hf_single_site.list_show_conv(beta, filestr='SB_PM_B{}', n_freq=5, xlim=2, skip=5)

Plots in individual figures for all interactions the DMFT loops

dmft.plot.hf_single_site.phases(beta_array)

Scatter plot of the DOS at Fermi level

Shows the phase diagram of the impurity model of DMFT

dmft.plot.hf_single_site.plot_fit_dos(beta, avg, filestr='SB_PM_B{}', xlim=2)

Plot the evolution of the Green’s function in DMFT iterations

dmft.plot.hf_single_site.show_conv(beta, u_int, filestr='SB_{simt}_B{beta}', n_freq=5, xlim=2, skip=5, simt='PM')

Plot the evolution of the Green’s function in DMFT iterations

Classes

class dmft.plot.hf_single_site.interp1d(x, y, kind='linear', axis=-1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False)

Interpolate a 1-D function.

x and y are arrays of values used to approximate some function f: y = f(x). This class returns a function whose call method uses interpolation to find the value of new points.

Note that calling interp1d with NaNs present in input values results in undefined behaviour.

Parameters:
  • x ((N,) array_like) – A 1-D array of real values.
  • y ((..,N,..) array_like) – A N-D array of real values. The length of y along the interpolation axis must be equal to the length of x.
  • kind (str or int, optional) – Specifies the kind of interpolation as a string (‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’ where ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of zeroth, first, second or third order) or as an integer specifying the order of the spline interpolator to use. Default is ‘linear’.
  • axis (int, optional) – Specifies the axis of y along which to interpolate. Interpolation defaults to the last axis of y.
  • copy (bool, optional) – If True, the class makes internal copies of x and y. If False, references to x and y are used. The default is to copy.
  • bounds_error (bool, optional) – If True, a ValueError is raised any time interpolation is attempted on a value outside of the range of x (where extrapolation is necessary). If False, out of bounds values are assigned fill_value. By default, an error is raised unless fill_value=”extrapolate”.
  • fill_value (array-like or (array-like, array_like) or "extrapolate", optional) –
    • if a ndarray (or float), this value will be used to fill in for requested points outside of the data range. If not provided, then the default is NaN. The array-like must broadcast properly to the dimensions of the non-interpolation axes.
    • If a two-element tuple, then the first element is used as a fill value for x_new < x[0] and the second element is used for x_new > x[-1]. Anything that is not a 2-element tuple (e.g., list or ndarray, regardless of shape) is taken to be a single array-like argument meant to be used for both bounds as below, above = fill_value, fill_value.

      New in version 0.17.0.

    • If “extrapolate”, then points outside the data range will be extrapolated.

      New in version 0.17.0.

  • assume_sorted (bool, optional) – If False, values of x can be in any order and they are sorted first. If True, x has to be an array of monotonically increasing values.
__call__()

See also

splrep, splev

UnivariateSpline
An object-oriented wrapper of the FITPACK routines.
interp2d
2-D interpolation

Examples

>>> import matplotlib.pyplot as plt
>>> from scipy import interpolate
>>> x = np.arange(0, 10)
>>> y = np.exp(-x/3.0)
>>> f = interpolate.interp1d(x, y)

>>> xnew = np.arange(0, 9, 0.1)
>>> ynew = f(xnew)   # use interpolation function returned by `interp1d`
>>> plt.plot(x, y, 'o', xnew, ynew, '-')
>>> plt.show()