[gf<imtime>] Matsubara imaginary time¶
This is a specialisation of gf for imaginary Matsubara time.
Synopsis¶
gf<imtime, Target, Opt>
The Target template parameter can take the following values:
| Target | Meaning |
|---|---|
| scalar_valued | The function is scalar valued (double, complex…). |
| matrix_valued [default] | The function is matrix valued. |
Domain & mesh¶
The domain is the set of real numbers between 0 and \(\beta\) since the function is periodic (resp. antiperiodic) for bosons (resp. fermions), i.e.
- \(G(\tau+\beta)=-G(\tau)\) for fermions
- \(G(\tau+\beta)=G(\tau)\) for bosons.
The domain is implemented in
The mesh is gf_mesh<imtime>.
Singularity¶
The singularity is a high frequency expansion, High-Frequency moments of the Green’s function.
Evaluation method¶
- Use a linear interpolation between the two closest point of the mesh.
- Return type:
- If Target==scalar_valued: a complex
- If Target==matrix_valued: an object modeling ImmutableMatrix concept.
- When the point is outside of the mesh, the evaluation of the gf returns:
- the evaluation of the high frequency tail
Data storage¶
- If Target==scalar_valued :
- data_t: 1d array of complex<double>.
- g.data()(i) is the value of g for the i-th point of the mesh.
- If Target==matrix_valued :
- data_t: 3d array (C ordered) of complex<double>.
- g.data()(i, range(), range()) is the value of g for the i-th point of the mesh.
TO DO: complex OR DOUBLE: FIX and document !!
HDF5 storage convention¶
h5 tag: ImTime