triqs.gfs.semicirc.g_semicirc_tau_adapquad

triqs.gfs.semicirc.g_semicirc_tau_adapquad(tau, beta, D, epsabs=0.0, epsrel=1e-13)

Semi-circular Green’s function on the imaginary-time axis via adaptive quadrature.

Uses scipy.integrate.quad() to evaluate the original integral

\[G(\tau) = -\int_{-D}^{D} \frac{e^{-\tau\omega}}{1 + e^{-\beta\omega}}\,\rho(\omega)\,d\omega\]

by splitting into \([-D,0]\) and \([0,D]\) to avoid overflow.

Parameters:

taufloat or array_like

Imaginary time(s), \(0 \le \tau \le \beta\).

betafloat

Inverse temperature.

Dfloat

Half-bandwidth.

epsabsfloat

Absolute error tolerance (default 0).

epsrelfloat

Relative error tolerance (default 1e-13).

Returns:

Gfloat or ndarray

Value of the Green’s function at the supplied imaginary times.