[GfLegendre] Matsubara Green’s function with Legendre polynomials

Reference

class triqs.gf.GfLegendre(**kw)

mesh: MeshLegendre, 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.

enforce_discontinuity(*args, **kw)

Signature : (gf_view<triqs::gfs::legendre,matrix_valued> gl, matrix_view<double> disc) -> None Modify the coefficient to adjust discontinuity

Warning

Arguments of __init__() must be documented.

HDF5 data scheme

The GfLegendre (Format= “GfLegendre”) 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 Legendre coefficient index i1, i2 are the indices
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’s function block
Note	string	Note

Example

from triqs.gf import *
from triqs.plot.mpl_interface import oplot,plt

# A Green's function on the Matsubara axis set to a semicircular
gw = GfImFreq(indices = [1], beta = 50)
gw << SemiCircular(half_bandwidth = 1)

# Create a Legendre Green's function with 40 coefficients
# and initialize it from gw
gl = GfLegendre(indices = [1], beta = 50, n_points = 40)
gl << MatsubaraToLegendre(gw)

# Plot the Legendre Green's function
oplot(gl, '-o')

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