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https://github.com/triqs/dft_tools
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73 lines
4.9 KiB
ReStructuredText
73 lines
4.9 KiB
ReStructuredText
.. highlight:: c
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.. _gf_tail:
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High frequency tail
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===========================
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Definition
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----------------------
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The tail of a Green's function is defined as the behavior of the Green's
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function :math:`G` at large Matsubara frequencies, namely
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.. math:: \mathbf{G}(i\omega_n) \stackrel {=}{\infty} \mathbf{a}_{-1}\cdot i\omega_n + \mathbf{a}_{0} +\mathbf{a}_{1}\cdot \frac{1}{ i\omega_n} +\mathbf{a}_{2}\cdot \frac{1}{ (i\omega_n)^2} +\dots
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Generically, the tail is parametrized by matrix-valued coefficients
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:math:`\mathbf{a}_{i}` (of size :math:`N_1\times N_2`\ )
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.. math:: t = \sum_{i=o_{min}}^{o_{max}} \mathbf{a}_i (i\omega_n)^{-i}
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Implementation
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--------------
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In TRIQS, the tail is implemented as an object ``tail``. Here is a simple example of use:
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.. compileblock::
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#include <Python.h>
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#include <iostream>
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#include <triqs/gfs/local/tail.hpp>
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int main(){
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int N1=1, N2=1;
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triqs::gfs::local::tail t(N1,N2);
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t.mask_view() = 5;//only coeffs from -1 to 5 are meaningful
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std::cout << t(0) << std::endl;
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t(2) = .5;
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std::cout << t << std::endl;
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}
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API
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****
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| Member | Description | Type |
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+=================================+========================================================================================+==========================+
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| data() | 3-dim array of the coefficients: ``data(i,n,m)`` :math:`=(\mathbf{a}_{i+o_{min}})_{nm}` | data_view_type |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| mask_view() | 2-dim (:math:`N_1 \times N_2`) array of the maximum non-zero indices | mask_view_type |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| order_min() | minimum order | long |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| order_max() | maximum order | long |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| size() | first dim of data() | size_t |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| shape() | shape of data() | shape_type |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| smallest_nonzeros() | order of the smallest_nonzero coefficient | long |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| is_decreasing_at_infinity() | true if the tail is decreasing at infinity | bool |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| operator() (int n) | matrix_valued coefficient :math:`(\mathbf{a}_i)_{nm}` | mv_type |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| get_or_zero (int n) | matrix_valued coefficient :math:`(\mathbf{a}_i)_{nm}` | const_mv_type |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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| evaluate(dcomplex const &omega) | value of the tail at frequency omega | arrays::matrix<dcomplex> |
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+---------------------------------+----------------------------------------------------------------------------------------+--------------------------+
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The tail is DefaultConstructible, H5Serializable and BoostSerializable.
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