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dft_tools/doc/reference/python/green/block/GfLegendre.rst
Olivier Parcollet f2c7d449cc First commit : triqs libs version 1.0 alpha1
for earlier commits, see TRIQS0.x repository.
2013-07-17 19:24:07 +02:00

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.. index::
single: Green's functions; block Green's function
module: gf_legendre
.. _GfLegendre:
Matsubara Green's function with Legendre polynomials (GfLegendre)
=====================================================================================
This object stores a matrix-valued Matsubara Green's function in imaginary time using
Legendre polynomials. It is connected to the usual imaginary-time Matsubara Green's
function through:
.. math::
G_{l, \alpha \beta} = \sqrt{2l+1} \int_0^\beta d\tau P_l (x(\tau)) G_{\alpha \beta}(\tau),
where :math:`x(\tau) = 2\tau/\beta -1` and the :math:`P_l` are the Legendre
polynomials. :math:`G_{\alpha \beta}(\tau)` is the :ref:`Matsubara Green's
function in imaginary time <GfImTime>`.
Reference
---------------
.. autoclass:: pytriqs.gf.local.GfLegendre
:members: density, enforce_discontinuity
HDF5 data scheme
^^^^^^^^^^^^^^^^^^
The GfLegendre (TRIQS_HDF5_data_scheme= "GfLegendre") is decomposed in the following objects :
========================= =========================== ===========================================================================
Name Type Meaning
========================= =========================== ===========================================================================
Mesh MeshGf The mesh
Tail TailGf The tail
Data 3d numpy of complex Data[i1,i2,n] is the element of the Green function where :
* i1, i2 are the indices
* n is the Legendre coefficient index
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
---------------
.. plot:: reference/python/green/block/green_legendre.py
:include-source:
:scale: 70