Hybridization fitting

adapol.hybfit.hybfit(Delta, iwn_vec, tol=None, Np=None, svdtol=1e-07, solver='lstsq', maxiter=500, mmin=4, mmax=50, verbose=False)[source]

The function for hybridization fitting.

Examples:

Fitting with \(N_p\) poles:
hybfit(Delta, iwn_vec, Np = Np)

Fitting with fixed error tolerance tol :
hybfit(Delta, iwn_vec, tol = tol)

Parameters:

Delta: np.array, \((N_w, N_\mathrm{orb}, N_\mathrm{orb})\): The input hybridization function in Matsubara frequency.
iwn_vec: np.array, \((N_w)\): The Matsubara frequency vector, complex-valued
svdtol: float, optional: Truncation threshold for bath orbitals while doing SVD of weight matrices in hybridization fitting default:1e-7
tol, Np, solver, maxiter, mmin, mmax, verbose:: see below in anacont

Returns:

bathenergy \(E\): np.array, \((N_b)\): Bath energy
bathhyb \(V\): np.array, \((N_b,N_{\mathrm{orb}})\): Bath hybridization
final_error: float: final fitting error
func: function: Hybridization function evaluator \(f(z) = \sum_n V_{ni}V_{nj}^*/(z-E_n).\)

Analytic continuation

adapol.anacont.anacont(Delta, iwn_vec, tol=None, Np=None, solver='lstsq', maxiter=500, mmin=4, mmax=50, verbose=False)[source]

The function for analytical continuation.

Examples:

Analytic continuation with \(N_p\) poles:
func = anacont(Np = Np)

Fitting with fixed error tolerance tol:
func = anacont(tol = tol)

Analytic continuation with improved accuracy:
fitting(Np = Np, flag = flag, solver = "sdp")

Parameters:

Delta: np.array, \((N_w, N_\mathrm{orb}, N_\mathrm{orb})\): The input hybridization function in Matsubara frequency.
iwn_vec: np.array, \((N_w,)\): The Matsubara frequency vector, complex-valued
tol: Fitting error tolreance, float: If tol is specified, the fitting will be conducted with fixed error tolerance tol. default: None
Np: number of poles, integer: If Np is specified, the fitting will be conducted with fixed number of poles Np. default: None Np needs to be an odd integer, and number of supoort points is Np + 1.
solver: string: The solver that is used for optimization. choices: “lstsq”, “sdp” default: “lstsq”
maxiter: int: maximum number of iterations default: 500
mmin, mmax: number of minimum or maximum poles, integer: default: mmin = 4, mmax = 50 if tol is specified, mmin and mmax will be used as the minimum and maximum number of poles. if Np is specified, mmin and mmax will not be used.
verbose: bool: whether to display optimization details default: False

Returns:

func: function: Analytic continuation function: \(f(z) = \sum_n \mathrm{Weight}[n]/(z-\mathrm{pol}[n]).\)
fitting_error: float: fitting error
pol: np.array, \((N_p,)\): poles obtained from fitting
weight: np.array, \((N_p, N_\mathrm{orb}, N_\mathrm{orb})\): weights obtained from fitting

TRIQS interface

adapol.hybfit.hybfit_triqs(Delta_triqs, tol=None, Np=None, svdtol=1e-07, solver='lstsq', maxiter=500, mmin=4, mmax=50, verbose=False, debug=False)[source]

The triqs interface for hybridization fitting. The function requires triqs package in python.

Examples:

Fitting with \(N_p\) poles:
hybfit_triqs(delta_triqs, Np = Np)

Fitting with fixed error tolerance tol :
hybfit_triqs(delta_triqs, tol = tol)

Parameters:

Delta_triqs: triqs Green’s function container: The input hybridization function in Matsubara frequency
debug: bool: return additional outputs for debugging. Default: False
svdtol: float, optional: Truncation threshold for bath orbitals while doing SVD of weight matrices in hybridization fitting default: 1e-7
tol, Np, solver, maxiter, mmin, mmax, verbose:: same as in hybfit

Returns:

bathhyb: np.array \((N_b, N_\mathrm{orb})\)

Bath hybridization

bathenergy: np.array \((N_b,)\)

Bath energy

Delta_fit: triqs Gf or BlockGf

Discretized hybridization function The input hybridization function in Matsubara frequency

if debug is True:

final_error: float: final fitting error
weight: np.array \((N_p, N_\mathrm{orb}, N_\mathrm{orb})\): weights obtained from fitting

adapol.anacont.anacont_triqs(Delta_triqs, tol=None, Np=None, solver='lstsq', maxiter=500, mmin=4, mmax=50, verbose=False, debug=False)[source]

The triqs interface for analytical continuation. The function requires triqs package in python.

Parameters:

Delta_triqs: triqs Green’s function container: The input hybridization function in Matsubara frequency
debug: bool: return additional outputs for debugging. Default: False
tol, Np, solver, maxiter, mmin, mmax, verbose:: same as in anacont

Returns:

func: function

Analytic continuation function: \(f(z) = \sum_n \mathrm{Weight}[n]/(z-\mathrm{pol}[n]).\)

if debug == True:

fitting_error: float: fitting error
pol: np.array, \((N_p,)\): poles obtained from fitting
weight: np.array, \((N_p, N_\mathrm{orb}, N_\mathrm{orb})\): weights obtained from fitting