triqs_ctseg::measure_gl¶
#include <triqs_ctseg.hpp>
class measure_gl
Measure for the Green’s function in Legendre basis
- The Legendre coefficients of the Green’s function and the improved estimator
- are defined as
\[X(l)=\sqrt{2l+1}\int_0^\beta d\tau\,P_l[x(\tau)]X(\tau)\]
with \(X=G^\sigma_{ab},F^\sigma_{ab}\), \(x(\tau)=2\tau/\beta-1\) and \(P_l(x)\) are the Legendre polynomials, defined in the [-1,1] interval.
- These measurements are controlled through the switches and parameter
measure_gl,measure_flandn_legendre_g.- The Legendre Green’s function may be transformed to the Matsubara basis
through the unitary transformation
\(G_a(i\omega_n) = \sum_{l\geq 0}T_{nl} G_a(l)\)where
\(T_{nl} = (-1)^ni^{l+1}\sqrt{2l+1}j_l\left(\frac{(2n+1)\pi}{2}\right)\)with the spherical Bessel functions \(j_l(z)\).
Public members¶
| params | const triqs_ctseg::qmc_parameters * | |
| config | const triqs_ctseg::configuration * | |
| gl | triqs_ctseg::g_l_t & | |
| fl | triqs_ctseg::g_l_t & | |
| fprefactor | std::shared_ptr<precompute_fprefactor> | |
| beta | double | |
| Z | double | |
| n_l | int | |
| Tn | triqs::utility::legendre_generator |