Tools for GFs
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triqs.gf.tools.conjugate(x)[source] Return the conjugate of a Green’s function
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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])
Parameters: g (BlockGf (of GfImFreq) or GfImFreq) – Non-interacting Green’s function. Returns: delta_iw – Hybridization function. Return type: BlockGf (of GfImFreq) or GfImFreq
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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(-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
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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.
Parameters:
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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)
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triqs.gf.tools.inverse(x)[source] Return the inverse of its argument, with proper treatement of lazy expressions.
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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(-eta * 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:
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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.
Parameters:
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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: - block_txtfiles (Rank 2 square np.array(str) or list[list[str]]) –
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triqs.gf.tools.transpose(x)[source] Return the transpose of a Green’s function