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