Analysis¶

We can get get the correlation functions directly from textsc{fortran}, and perform the subsequent analysis with:

# DOS correlation, fortran call
corr_DOS = tipsi.corr_DOS(sample, config)

# DOS correlation analysis
energies_DOS, DOS = tipsi.analyze_corr_DOS(config, corr_DOS)

# AC conductivity correlation, fortran call
corr_AC = tipsi.corr_AC(sample, config)

# AC conductivity correlation analysis
omegas_AC, AC = tipsi.analyze_corr_AC(config, corr_AC)

Alternatively, we can read the correlation functions from file in a separate Python script:

timestamp = "1522172330" # set to output timestamp

# read Config object
config = tipsi.read_config("sim_data/" + timestamp + "config.pkl")

# get DOS
corr_DOS = tipsi.read_corr_DOS("sim_data/" + timestamp + "corr_DOS.dat")
energies_DOS, DOS = tipsi.analyze_corr_DOS(config, corr_DOS)

Correlation function analysis¶

tipsi.analysis.analyze_corr_DOS(config, corr_DOS, window=<function window_Hanning>)¶

Function for analyzing the DOS correlation function.

Parameters:

config (Config object) – contains TBPM configuration parameters
corr_DOS (list of complex floats) – DOS correlation function
window (function, optional) – window function for integral; default: window_Hanning

Returns:

energies (list of floats) – energy values
DOS (list of floats) – DOS values corresponding to energies

tipsi.analysis.analyze_corr_AC(config, corr_AC, window=<function window_exp>)¶

Function for analyzing the AC conductivity correlation function.

Parameters:

config (Config object) – contains TBPM configuration parameters
corr_AC ((4,n) list of complex floats) – AC conductivity correlation function
window (function, optional) – window function for integral; default: window_exp

Returns:

omegas (list of floats) – omega values
AC ((4,n) list of floats) – AC conductivity values corresponding to omegas, for 4 directions (xx, xy, yx, yy, respectively)

tipsi.analysis.AC_imag(AC_real)¶

Get the imaginary part of the AC conductivity from the real part using the Kramers-Kronig relations (the Hilbert transform).

Parameters:	AC_real (array of floats) – Re(sigma)
Returns:	Im(sigma)
Return type:	array of floats

tipsi.analysis.analyze_corr_DC(config, corr_DOS, corr_DC, window_DOS=<function window_Hanning>, window_DC=<function window_exp>)¶

Function for analyzing the DC correlation function.

Parameters:

config (Config object) – contains TBPM configuration parameters
corr_DOS ((n_t_steps) list of floats) – DOS correlation function
corr_DC ((2, n_energies, n_t_steps) list of floats) – DC conductivity correlation function
window_DOS (function, optional) – window function for DOS integral; default: window_Hanning
window_DC (function, optional) – window function for DC integral; default: window_exp

Returns:

energies (list of floats) – energy values
DC ((2, n_energies) list of floats) – DC conductivity values

tipsi.analysis.analyze_corr_dyn_pol(config, corr_dyn_pol, window=<function window_exp_ten>)¶

Function for analyzing the dynamical polarization correlation function.

Parameters:

config (Config object) – contains TBPM configuration parameters
corr_dyn_pol ((n_q_points, n_t_steps) list of floats) – dynamical polarization correlation function
window (function, optional) – window function for integral; default: window_exp_ten

Returns:

q_points (list of floats) – q-point values
omegas (list of floats) – omega values
dyn_pol ((n_q_points, n_omegas) list of complex floats) – dynamical polarization values corresponding to q-points and omegas

tipsi.analysis.get_dielectric_function(config, dyn_pol)¶

Function for analyzing the DOS correlation function.

Parameters:	sample (Sample object) – contains sample information config (Config object) – contains TBPM configuration parameters dyn_pol ((n_q_points, n_t_steps) list of complex floats) – dynamical polarization values
Returns:	epsilon – dielectric function
Return type:	(n_q_points, n_omegas) list of complex floats

Reading from file¶

tipsi.input.read_config(filename)¶

Read Config object from file

Parameters:	filename (string) – read Config object from this file
Returns:
Return type:	Config object

tipsi.input.read_sample(filename, lattice=None, bc_func=<function bc_default>, nr_processes=1)¶

Read Sample object from file

Parameters:	filename (string) – read Sample object from this file lattice (Lattice object) – lattice corresponding to the sample; default: None bc_func (function) – boundary conditions function; default: bc_default nr_processes (integer) – number of processes to use for numerically expensive Sample methods; default: 1
Returns:
Return type:	Sample object

tipsi.input.read_corr_DOS(filename)¶

Read DOS correlation from file

Parameters:	filename (string) – read correlation values from this file
Returns:	corr_DOS – the DOS correlation function
Return type:	(n_timesteps) list of complex floats

tipsi.input.read_corr_AC(filename)¶

Read AC correlation from file

Parameters:	filename (string) – read correlation values from this file
Returns:	corr_AC – the AC correlation function
Return type:	(4, n_timesteps) list of complex floats

tipsi.input.read_corr_DC(filename)¶

Read DC conductivity correlation from file

Parameters:	filename (string) – read DC conductivity correlation values from this file
Returns:	corr_DC – the dynamical polarization correlation function
Return type:	(2, n_energies, n_t_steps) list of complex floats

tipsi.input.read_corr_dyn_pol(filename)¶

Read dynamical polarization correlation from file

Parameters:	filename (string) – read correlation values from this file
Returns:	corr_dyn_pol – the dynamical polarization correlation function
Return type:	(n_q_points, n_timesteps) list of complex floats

Window functions¶

tipsi.analysis.window_Hanning(i, N)¶

Hanning window.

Parameters:	i (integer) – summation index N (integer) – total length of summation
Returns:	Hanning window value
Return type:	float

tipsi.analysis.window_exp(i, N)¶

Exponential window.

Parameters:	i (integer) – summation index N (integer) – total length of summation
Returns:	exponential window value
Return type:	float

tipsi.analysis.window_exp_ten(i, N)¶

Window function given by exponential of 10.

Parameters:	i (integer) – summation index N (integer) – total length of summation
Returns:	exponential window value
Return type:	float

Output¶

tipsi.output.plot_wf(wf, sample, filename, site_size=5, fig_dpi=300, colorbar=False)¶

Plot wavefunction

Parameters:	wf (list of complex floats) – wavefunction sample (Sample object) – geometric information of the sample filename (string) – image file name site_size (float) – site size; default 5 fig_dpi (float) – dpi of output figure; default 300 colorbar (bool) – add colorbar to figure; default False