Python 石墨烯边缘磁性Hatree

Hatree_Fock自洽过程尽可能向量化优化

import numpy as np
from numpy import exp, pi
from numpy.linalg import eigh
import matplotlib.pylab as plt
from numba import njit@njit
def Fermi(E, mu, T):return 1/(np.exp((E - mu)/T) + 1)@njit
def tridiag_block_matrix(H, c, u, d):# c, u, d are center, upper and lower blocksN, _ = H.shapen, _ = c.shapeH[0:n, 0:n] = cfor i in range(n, N, n):H[i:i+n, i:i+n] = cH[i-n:i, i:i+n] = dH[i:i+n, i-n:i] = ureturn H@njit
def H0_Graphene(H, k, t = -1):A = np.array([[0, t*(1+exp(-1j* k))], [t*(1+ exp(1j*k)), 0]])B = np.array([[0, 0], [t, 0]])return tridiag_block_matrix(H, A, B, B.T)# Hatree_Fork 自洽计算过程
def Hatree_Fock(H, ks, Nup_avg, Ndown_avg, U, T = 0.001, mu = 0,  ncc = 20):m, _ = Nup_avg.shapenk = ks.sizefor ic in range(ncc):Nup_avg_tmp = np.zeros((m,m), dtype='double')Ndown_avg_tmp = np.zeros((m,m), dtype='double')for i in range(nk):Hk0 = H0_Graphene(H, ks[i])Hk_up = Hk0 + U * (Ndown_avg - 0.5 * np.eye(m))Hk_down = Hk0 + U * (Nup_avg - 0.5 * np.eye(m))Ek_up, Ak_up = eigh(Hk_up)Ek_down, Ak_down = eigh(Hk_down)fermi_up = Fermi(Ek_up,mu,T).reshape(1,m)fermi_down = Fermi(Ek_down,mu,T).reshape(1,m)Nk_up = (Ak_up*Ak_up.conj()*fermi_up).sum(axis=1,dtype='double')Nk_down = (Ak_down*Ak_down.conj()*fermi_down).sum(axis=1,dtype='double')Nup_avg_tmp += np.diag(Nk_up)Ndown_avg_tmp += np.diag(Nk_down)Nup_avg = Nup_avg_tmp/nkNdown_avg = Ndown_avg_tmp/nkif ic % 5==0:print(f"已经完成{ic}次迭代")return Nup_avg, Ndown_avgdef calculated_band():N = 128m = 2 * NH = np.zeros((m, m), dtype = np.complex64)nk = 128ks = np.linspace(0, 2*pi, nk)U = 1.5Nup_avg = 0.5 * np.eye(m)Ndown_avg = 0.5 * np.eye(m)Nup_avg[0, 0] = 0.7Ndown_avg[0, 0] = 0.3Nup_avg[-1, -1] = 0.3Ndown_avg[-1, -1] = 0.7Nup_avg, Ndown_avg = Hatree_Fock(H, ks, Nup_avg, Ndown_avg, U)bandUp = np.zeros((nk, m))bandDown = np.zeros((nk, m))for i in range(nk):Hk0 = H0_Graphene(H, ks[i])Hk_up = Hk0 + U * (Ndown_avg - 0.5 * np.eye(m)) Hk_down = Hk0 + U * (Nup_avg - 0.5 * np.eye(m))Ek_up, _ = eigh(Hk_up)Ek_down, _ = eigh(Hk_down)bandUp[i, :] = Ek_upbandDown[i, :] = Ek_downplt.plot(bandUp, color = "red")plt.plot(bandDown, color = "blue")plt.show()plt.plot(Nup_avg - Ndown_avg)plt.show()# print(Nup_avg[0, 0], Nup_avg[-1, -1])# print(Ndown_avg[0, 0], Nup_avg[-1, -1])if __name__ == '__main__':calculated_band()

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Python 石墨烯边缘磁性Hatree_Fock计算

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