triqs_ctseg::measure_gt
#include <triqs_ctseg.hpp>
class measure_gt
Measure for the Green’s function in imaginary time
The imaginary-time Green’s function is defined as
\[G^\sigma_{ab}(\tau) = -\langle T_\tau
c_{a\sigma}(\tau)c_{b\sigma}^\dagger(0) \rangle\]
and the corresponding improved estimator is given by
\[F_{ab}^{\sigma}(\tau) = -\int_0^\beta d\tilde{\tau} \sum_{c\sigma'} \langle
T_\tau n_{c\sigma'}(\tilde{\tau})
\mathcal{U}^{\sigma\sigma'}_{ac}(\tilde{\tau}-\tau)
c_{a\sigma}(\tau)c_{b\sigma'}^\dagger(0) \rangle\]
- The imaginary-time measurement is most efficient. The performance of the
algorithm does not scale with the number of points in the grid on which it is measured, so this number can and should be chosen large. By Nyquist’s theorem, the Fourier transform will be correctly reproduce the function in the frequency domain on the first \(N_\omega\approx N_\tau/4\pi\) frequencies.
- These measurements are turned on by setting
measure_gtandmeasure_ft to
true, respectively. *The number of time points on the grid is specified throughn_tauand is the same for both observables.