triqs.gf.tools.discretize_bath

triqs.gf.tools.discretize_bath(delta_in, Nb, eps0=3, V0=None, tol=1e-15, maxiter=10000, cmplx=False, method='BFGS')

Discretize a given hybridization function using Nb bath sites.

The discretized hybridization is constructed as .. math:: Delta_{kl}^{disc} (i omega_n) = sum_{j=1}^{Nb} V_{kj} S V_{jl}^* . where S is either: .. math:: [i omega_n - eps_j]^{-1} for MeshImFreq or .. math:: - exp(-tau * eps_j) / (1 + exp(-eta * eps_j) ) for MeshImTime.

The hoppings V and energies eps are chosen to minimize the norm .. math:: left[

rac{1}{sqrt(N)} sum_{i omega_n}^{N} | Delta^{disc} (i omega_n) - Delta (i omega_n) |^2 ight]^{ rac{1}{2}}

and for MeshImTime .. math:: left[

rac{1}{sqrt(N)} sum_{ au}^{N} | Delta^{disc} ( au) - Delta ( au) |^2 ight]^{ rac{1}{2}}

This minimization is performed with the given tolerance using scipy.optimize.minimize or the scipy.optimize.basinhopping frontend.

delta_inGf or BlockGf

Matsubara or imaginary-time hybridization function to discretize

Nbint

Number of bath sites per Gf block

eps0: float or list(float), default=3.0

Approximate bandwith or initial guesses for bath energies.

V0float or np.ndarray (shape norb X Nb), optional

If float: initial guess used for all hopping values. If np.ndarray: initial guess for V. Otherwise use the cholesky decomposition of .. math:: lim_{omega->infty} iomega*Delta(iomega) or .. math:: -Delta( au=0^+) - Delta( au=eta^-) to obtain an initial guess for V.

tolfloat, default=1e-15

Tolerance for scipy minimize on data to optimize (xatol / ftol)

maxiterint, default=10000

Maximum number of optimization steps

complxbool, default=False

Allow the hoppings V to be complex

methodstring, default=BFGS

Method for minimizing the function. Should be one of ‘BFGS’, ‘Nelder-Mead’ and ‘basinhopping’.

V_optnp.array (shape norb x Nb) or list thereof

Optimized bath hoppings

eps_optlist(float) or list(list(float)

Optimized bath energies (sorted)

delta_discGf or BlockGf

Discretized hybridization function