[GfImFreq] Matsubara Green’s function in imaginary frequencies¶

Reference¶

class pytriqs.gf.GfImFreq(**kw)[source]¶

mesh: MeshImFreq, optional: The mesh of the Green function If not present, it will be constructed from the parameters beta, indices, [n_points], [statistic]
data: numpy.array, optional: The data of the Gf. Must be of dimension mesh.rank + target_rank. Incompatible with target_shape
target_shape: list of int, optional: Shape of the target space. Incompatible with data
is_real: bool: Is the Green function real valued ? If true, and target_shape is set, the data will be real. No effect with the parameter data.
indices: GfIndices or list of str or list of list of str, Optional: Optional string indices for the target space, to allow e.g g[‘eg’, ‘eg’] list of list of str: the list of indices for each dimension. list of str: all indices are assumed to be the same for all dimensions.
name: str: The name of the Green function. For plotting.

density(*args, **kwargs)¶

Compute the density matrix of the Greens function

Parameters:	beta (float, optional) – Used for finite temperature density calculation with `MeshReFreq`.
Returns:	density_matrix – Single particle density matrix with shape `target_shape`.
Return type:	ndarray

Notes

Only works for single mesh Greens functions with a, Matsubara, real-frequency, or Legendre mesh.

set_from_fourier(*args, **kw)¶

Fills self with the Fourier transform of g_in

Signature : (gf_view<imtime,scalar_valued> g_out, gf_view<imfreq,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imtime,scalar_valued> g_out, block_gf_view<imfreq,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imtime,scalar_valued> g_out, block2_gf_view<imfreq,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imtime,scalar_valued> g_out, gf_view<imfreq,scalar_valued> g_in, array_const_view<dcomplex,1+scalar_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<imfreq,scalar_valued> g_out, gf_view<imtime,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imfreq,scalar_valued> g_out, block_gf_view<imtime,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imfreq,scalar_valued> g_out, block2_gf_view<imtime,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imfreq,scalar_valued> g_out, gf_view<imtime,scalar_valued> g_in, array_const_view<dcomplex,1+scalar_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<retime,scalar_valued> g_out, gf_view<refreq,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<retime,scalar_valued> g_out, block_gf_view<refreq,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<retime,scalar_valued> g_out, block2_gf_view<refreq,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<retime,scalar_valued> g_out, gf_view<refreq,scalar_valued> g_in, array_const_view<dcomplex,1+scalar_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<refreq,scalar_valued> g_out, gf_view<retime,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<refreq,scalar_valued> g_out, block_gf_view<retime,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<refreq,scalar_valued> g_out, block2_gf_view<retime,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<refreq,scalar_valued> g_out, gf_view<retime,scalar_valued> g_in, array_const_view<dcomplex,1+scalar_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<cyclic_lattice,scalar_valued> g_out, gf_view<brillouin_zone,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<cyclic_lattice,scalar_valued> g_out, block_gf_view<brillouin_zone,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<cyclic_lattice,scalar_valued> g_out, block2_gf_view<brillouin_zone,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<brillouin_zone,scalar_valued> g_out, gf_view<cyclic_lattice,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<brillouin_zone,scalar_valued> g_out, block_gf_view<cyclic_lattice,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<brillouin_zone,scalar_valued> g_out, block2_gf_view<cyclic_lattice,scalar_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imtime,matrix_valued> g_out, gf_view<imfreq,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imtime,matrix_valued> g_out, block_gf_view<imfreq,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imtime,matrix_valued> g_out, block2_gf_view<imfreq,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imtime,matrix_valued> g_out, gf_view<imfreq,matrix_valued> g_in, array_const_view<dcomplex,1+matrix_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<imfreq,matrix_valued> g_out, gf_view<imtime,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imfreq,matrix_valued> g_out, block_gf_view<imtime,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imfreq,matrix_valued> g_out, block2_gf_view<imtime,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imfreq,matrix_valued> g_out, gf_view<imtime,matrix_valued> g_in, array_const_view<dcomplex,1+matrix_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<retime,matrix_valued> g_out, gf_view<refreq,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<retime,matrix_valued> g_out, block_gf_view<refreq,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<retime,matrix_valued> g_out, block2_gf_view<refreq,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<retime,matrix_valued> g_out, gf_view<refreq,matrix_valued> g_in, array_const_view<dcomplex,1+matrix_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<refreq,matrix_valued> g_out, gf_view<retime,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<refreq,matrix_valued> g_out, block_gf_view<retime,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<refreq,matrix_valued> g_out, block2_gf_view<retime,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<refreq,matrix_valued> g_out, gf_view<retime,matrix_valued> g_in, array_const_view<dcomplex,1+matrix_valued::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<cyclic_lattice,matrix_valued> g_out, gf_view<brillouin_zone,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<cyclic_lattice,matrix_valued> g_out, block_gf_view<brillouin_zone,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<cyclic_lattice,matrix_valued> g_out, block2_gf_view<brillouin_zone,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<brillouin_zone,matrix_valued> g_out, gf_view<cyclic_lattice,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<brillouin_zone,matrix_valued> g_out, block_gf_view<cyclic_lattice,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<brillouin_zone,matrix_valued> g_out, block2_gf_view<cyclic_lattice,matrix_valued> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imtime,tensor_valued<3>> g_out, gf_view<imfreq,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imtime,tensor_valued<3>> g_out, block_gf_view<imfreq,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imtime,tensor_valued<3>> g_out, block2_gf_view<imfreq,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imtime,tensor_valued<3>> g_out, gf_view<imfreq,tensor_valued<3>> g_in, array_const_view<dcomplex,1+tensor_valued<3>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<imfreq,tensor_valued<3>> g_out, gf_view<imtime,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imfreq,tensor_valued<3>> g_out, block_gf_view<imtime,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imfreq,tensor_valued<3>> g_out, block2_gf_view<imtime,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imfreq,tensor_valued<3>> g_out, gf_view<imtime,tensor_valued<3>> g_in, array_const_view<dcomplex,1+tensor_valued<3>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<retime,tensor_valued<3>> g_out, gf_view<refreq,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<retime,tensor_valued<3>> g_out, block_gf_view<refreq,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<retime,tensor_valued<3>> g_out, block2_gf_view<refreq,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<retime,tensor_valued<3>> g_out, gf_view<refreq,tensor_valued<3>> g_in, array_const_view<dcomplex,1+tensor_valued<3>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<refreq,tensor_valued<3>> g_out, gf_view<retime,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<refreq,tensor_valued<3>> g_out, block_gf_view<retime,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<refreq,tensor_valued<3>> g_out, block2_gf_view<retime,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<refreq,tensor_valued<3>> g_out, gf_view<retime,tensor_valued<3>> g_in, array_const_view<dcomplex,1+tensor_valued<3>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<cyclic_lattice,tensor_valued<3>> g_out, gf_view<brillouin_zone,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<cyclic_lattice,tensor_valued<3>> g_out, block_gf_view<brillouin_zone,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<cyclic_lattice,tensor_valued<3>> g_out, block2_gf_view<brillouin_zone,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<brillouin_zone,tensor_valued<3>> g_out, gf_view<cyclic_lattice,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<brillouin_zone,tensor_valued<3>> g_out, block_gf_view<cyclic_lattice,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<brillouin_zone,tensor_valued<3>> g_out, block2_gf_view<cyclic_lattice,tensor_valued<3>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imtime,tensor_valued<4>> g_out, gf_view<imfreq,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imtime,tensor_valued<4>> g_out, block_gf_view<imfreq,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imtime,tensor_valued<4>> g_out, block2_gf_view<imfreq,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imtime,tensor_valued<4>> g_out, gf_view<imfreq,tensor_valued<4>> g_in, array_const_view<dcomplex,1+tensor_valued<4>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<imfreq,tensor_valued<4>> g_out, gf_view<imtime,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<imfreq,tensor_valued<4>> g_out, block_gf_view<imtime,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<imfreq,tensor_valued<4>> g_out, block2_gf_view<imtime,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<imfreq,tensor_valued<4>> g_out, gf_view<imtime,tensor_valued<4>> g_in, array_const_view<dcomplex,1+tensor_valued<4>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<retime,tensor_valued<4>> g_out, gf_view<refreq,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<retime,tensor_valued<4>> g_out, block_gf_view<refreq,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<retime,tensor_valued<4>> g_out, block2_gf_view<refreq,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<retime,tensor_valued<4>> g_out, gf_view<refreq,tensor_valued<4>> g_in, array_const_view<dcomplex,1+tensor_valued<4>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<refreq,tensor_valued<4>> g_out, gf_view<retime,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<refreq,tensor_valued<4>> g_out, block_gf_view<retime,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<refreq,tensor_valued<4>> g_out, block2_gf_view<retime,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<refreq,tensor_valued<4>> g_out, gf_view<retime,tensor_valued<4>> g_in, array_const_view<dcomplex,1+tensor_valued<4>::rank> known_moments) -> None: Fills self with the Fourier transform of g_in with known high-frequency moments
Signature : (gf_view<cyclic_lattice,tensor_valued<4>> g_out, gf_view<brillouin_zone,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<cyclic_lattice,tensor_valued<4>> g_out, block_gf_view<brillouin_zone,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<cyclic_lattice,tensor_valued<4>> g_out, block2_gf_view<brillouin_zone,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (gf_view<brillouin_zone,tensor_valued<4>> g_out, gf_view<cyclic_lattice,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block_gf_view<brillouin_zone,tensor_valued<4>> g_out, block_gf_view<cyclic_lattice,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in
Signature : (block2_gf_view<brillouin_zone,tensor_valued<4>> g_out, block2_gf_view<cyclic_lattice,tensor_valued<4>> g_in) -> None: Fills self with the Fourier transform of g_in

set_from_legendre(*args, **kw)¶

Fills self with the legendre transform of gl

Signature : (gf_view<imfreq,scalar_valued> gw, gf_view<triqs::gfs::legendre,scalar_valued> gl) -> None: Fills self with the legendre transform of gl
Signature : (gf_view<imtime,scalar_valued> gt, gf_view<triqs::gfs::legendre,scalar_valued> gl) -> None: Fills self with the legendre transform of gl
Signature : (gf_view<imfreq,matrix_valued> gw, gf_view<triqs::gfs::legendre,matrix_valued> gl) -> None: Fills self with the legendre transform of gl
Signature : (gf_view<imtime,matrix_valued> gt, gf_view<triqs::gfs::legendre,matrix_valued> gl) -> None: Fills self with the legendre transform of gl
Signature : (gf_view<imfreq,tensor_valued<3>> gw, gf_view<triqs::gfs::legendre,tensor_valued<3>> gl) -> None: Fills self with the legendre transform of gl
Signature : (gf_view<imtime,tensor_valued<3>> gt, gf_view<triqs::gfs::legendre,tensor_valued<3>> gl) -> None: Fills self with the legendre transform of gl
Signature : (gf_view<imfreq,tensor_valued<4>> gw, gf_view<triqs::gfs::legendre,tensor_valued<4>> gl) -> None: Fills self with the legendre transform of gl
Signature : (gf_view<imtime,tensor_valued<4>> gt, gf_view<triqs::gfs::legendre,tensor_valued<4>> gl) -> None: Fills self with the legendre transform of gl

Warning

Arguments of __init__() must be documented.

HDF5 data scheme¶

The GfImFreq (TRIQS_HDF5_data_scheme= “GfImFreq”) is decomposed in the following objects:

Name	Type	Meaning
Mesh	MeshGf	The mesh
Data	3d numpy of complex	Data[n,i1,i2] is the element of the Green function where: n is the Matsubara index i1, i2 are the indices For real GF in time, we store only starting from n=0 and the rest is deduced by symmetry
IndicesL,IndicesR	string	The Python repr of the indices, e.g. (1,2), or (1,) repr(this_string) reproduces the indices
Name	string	Name of the Green function block
Note	string	Note

Example¶

from pytriqs.gf import GfImFreq, SemiCircular

g = GfImFreq(indices = ['eg1','eg2'], beta = 50, n_points = 1000, name = "egBlock")

g['eg1','eg1'] = SemiCircular(half_bandwidth = 1)
g['eg2','eg2'] = SemiCircular(half_bandwidth = 2)

from pytriqs.plot.mpl_interface import oplot, plt
oplot(g, '-o', x_window = (0,10))
plt.ylim(-2,1)

(Source code, png, hires.png, pdf)

../../../../../../_images/green_imfreq.png

triqs

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[GfImFreq] Matsubara Green’s function in imaginary frequencies¶

Reference¶

HDF5 data scheme¶

Example¶