def test_pole(self):
T = 0.1
w_n = self.matsubara(T)
E = 0.3
Sigma = w_n * 0
Sigma0 = 0
N = density(w_n, E, Sigma, Sigma0)
self.assertEqual(N, self.fermi(E/T))
def test_zero(self):
T = 0.01
w_n = self.matsubara(T)
E = 0
Sigma = w_n * 0
Sigma0 = 0
N = density(w_n, E, Sigma, Sigma0)
self.assertEqual(N, 0.5)
def test_pole(self):
T = 0.1
w_n = self.matsubara(T)
E = 0.3
Sigma = w_n * 0
Sigma0 = 0
N = density(w_n, E, Sigma, Sigma0)
self.assertEqual(N, self.fermi(E / T))
def test_zero(self):
T = 0.01
w_n = self.matsubara(T)
E = 0
Sigma = w_n * 0
Sigma0 = 0
N = density(w_n, E, Sigma, Sigma0)
self.assertEqual(N, 0.5)
def test_sigma_pole(self):
T = 0.05
w_n = self.matsubara(T, N = 10000)
E = 0.3
V2 = 0.5
Sigma0 = 0.314159
Sigma = V2/(1j*w_n) + Sigma0
N = density(w_n, E, Sigma, Sigma0)
a = (E+Sigma0 + np.sqrt((E+Sigma0)**2 + 4*V2))/2
b = (E+Sigma0 - np.sqrt((E+Sigma0)**2 + 4*V2))/2
Nref = a/(a-b) * self.fermi(a/T) - b/(a-b) * self.fermi(b/T)
self.assertAlmostEqual(N, Nref)
def test_sigma_pole(self):
T = 0.05
w_n = self.matsubara(T, N=10000)
E = 0.3
V2 = 0.5
Sigma0 = 0.314159
Sigma = V2 / (1j * w_n) + Sigma0
N = density(w_n, E, Sigma, Sigma0)
a = (E + Sigma0 + np.sqrt((E + Sigma0)**2 + 4 * V2)) / 2
b = (E + Sigma0 - np.sqrt((E + Sigma0)**2 + 4 * V2)) / 2
Nref = a / (a - b) * self.fermi(a / T) - b / (a - b) * self.fermi(
b / T)
self.assertAlmostEqual(N, Nref)
