Tools for GFs
- triqs.gf.tools.conjugate(x)[source]
Return the conjugate of a Green’s function
- triqs.gf.tools.delta(g)[source]
Compute Delta_iw from G0_iw. CAUTION: This function assumes the following properties of g
The diagonal components of g should decay as 1/iOmega
g should fullfill the property g[iw][i,j] = conj(g[-iw][j,i])
- triqs.gf.tools.discretize_bath(delta_in, Nb, eps0=3, V0=None, tol=1e-15, maxiter=10000, cmplx=False, method='BFGS')[source]
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(-beta * eps_j) ) for MeshImTime.
The hoppings V and energies eps are chosen to minimize the norm .. math:: left[ frac{1}{sqrt(N)} sum_{i omega_n}^{N} | Delta^{disc} (i omega_n) - Delta (i omega_n) |^2 right]^{frac{1}{2}} and for MeshImTime .. math:: left[ frac{1}{sqrt(N)} sum_{tau}^{N} | Delta^{disc} (tau) - Delta (tau) |^2 right]^{frac{1}{2}} This minimization is performed with the given tolerance using scipy.optimize.minimize or the scipy.optimize.basinhopping frontend.
- Parameters:
delta_in (Gf or BlockGf) – Matsubara or imaginary-time hybridization function to discretize
Nb (int) – Number of bath sites per Gf block
eps0 (float or list(float), default=3.0) – Approximate bandwith or initial guesses for bath energies.
V0 (float 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(tau=0^+) - Delta(tau=beta^-) to obtain an initial guess for V.
tol (float, default=1e-15) – Tolerance for scipy minimize on data to optimize (xatol / ftol)
maxiter (int, default=10000) – Maximum number of optimization steps
complx (bool, default=False) – Allow the hoppings V to be complex
method (string, default=BFGS) – Method for minimizing the function. Should be one of ‘BFGS’, ‘Nelder-Mead’ and ‘basinhopping’.
- Returns:
V_opt (np.array (shape norb x Nb) or list thereof) – Optimized bath hoppings
eps_opt (list(float) or list(list(float)) – Optimized bath energies (sorted)
delta_disc (Gf or BlockGf) – Discretized hybridization function
- triqs.gf.tools.dyson(**kwargs)[source]
Solve Dyson’s equation for given two of G0_iw, G_iw and Sigma_iw to yield the third.
- triqs.gf.tools.fit_legendre(g_t, order=10)[source]
General fit of a noisy imaginary time Green’s function to a low order Legendre expansion in imaginary time.
Only Hermiticity is imposed on the fit, so discontinuities has to be fixed separately (see the method enforce_discontinuity)
Author: Hugo U.R. Strand
- Parameters:
g_t (TRIQS imaginary time Green's function (matrix valued)) – Imaginary time Green’s function to fit (possibly noisy binned data)
order (int) – Maximal order of the fitted Legendre expansion
- Returns:
g_l – Fitted Legendre Green’s function with order order
- Return type:
TRIQS Legendre polynomial Green’s function (matrix valued)
- triqs.gf.tools.inverse(x)[source]
Return the inverse of its argument, with proper treatement of lazy expressions.
- triqs.gf.tools.make_delta(V, eps, mesh, block_names=None)[source]
Create a hybridization function from given hoppings and bath energies 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(-beta * eps_j) ) for MeshImTime
- Parameters:
V (np.array (shape Norb x NB) or list thereof) – Bath hopping matrix or matrix for each Gf block
eps (list(float) or list(list(float))) – Bath energies or energies for each Gf block
mesh (MeshImFreq or MeshImTime) – Mesh of the hybridization function
block_names (list(str)) – List of block names, used if V, eps are lists
- Returns:
delta – Hybridization function on given mesh
- Return type:
- triqs.gf.tools.make_zero_tail(g, n_moments=10)[source]
Return a container for the high-frequency coefficients of a given Green function initialized to zero.
- triqs.gf.tools.read_gf_from_txt(block_txtfiles, block_name)[source]
Read a GfReFreq from text files with the format (w, Re(G), Im(G)) for a single block.
Notes
A BlockGf must be constructed from multiple GfReFreq objects if desired. The mesh must be the same for all files read in. Non-uniform meshes are not supported.
- Parameters:
block_txtfiles (Rank 2 square np.array(str) or list[list[str]]) –
The text files containing the GF data that need to read for the block. e.g. [[‘up_eg1.dat’]] for a one-dimensional block and
- [[‘up_eg1_1.dat’,’up_eg2_1.dat’],
[‘up_eg1_2.dat’,’up_eg2_2.dat’]] for a 2x2 block.
block_name (str) – Name of the block.
- Returns:
g – The real frequency Green’s function read in.
- Return type:
- triqs.gf.tools.transpose(x)[source]
Return the transpose of a Green’s function