gftool.pole_gf_tau_b

gftool.pole_gf_tau_b(tau, poles, weights, beta)

Bosonic imaginary time Green’s function given by a finite number of poles.

The bosonic Green’s function is given by G(tau) = -(1 + bose_fct(poles, beta))*exp(-poles*tau)

Parameters:

tau(…) float array_like

Green’s function is evaluated at imaginary times tau. Only implemented for \(τ ∈ [0, β]\).

poles, weights(…, N) float array_like

Position and weight of the poles. The real part of the poles needs to be positive poles.real > 0.

betafloat

Inverse temperature.

Returns:

(…) float np.ndarray

Imaginary time Green’s function.

Raises:

ValueError

If any poles.real <= 0.

See also

pole_gf_z

Corresponding commutator Green’s function.

Examples

>>> beta = 10
>>> tau = np.linspace(0, beta, num=1000)
>>> gf_tau = gt.pole_gf_tau_b(tau, .5, 1., beta=beta)

The integrated imaginary time Green’s function gives -np.sum(weights/poles)

>>> np.trapz(gf_tau, x=tau)
-2.0000041750107735

>>> import matplotlib.pyplot as plt
>>> __ = plt.plot(tau, gf_tau)
>>> __ = plt.xlabel('τ')
>>> plt.show()

(png, pdf)