问hermitian矩阵ARPACK的奇异性质

EN

import scipy.sparse as sparse
import scipy
import numpy
import numpy as np
import math
from scipy.special import binom
import cmath
import sympy
import matplotlib.pyplot as plt
import pylab
from copy import *
from numpy import linalg as LA



M=5#DIMENSION OF THE MATRIX


def tunneling(phase):#HAMILTONIAN MATRIX
    Matrix_hop = [[0 for x in range(M)] for y in range(M)]
    for i in range(M):
            if i+1==M:
                Matrix_hop[i][0] = -1.0
                Matrix_hop[i][i-1] = -1.0
        else:
                Matrix_hop[i][i+1] = -1.0
                Matrix_hop[i][i-1] = -1.0
    Matrix_hop[0][M-1]=-1.0*cmath.exp(1j*phase)
    Matrix_hop[M-1][0]=-1.0*cmath.exp(-1j*phase)
    return Matrix_hop 

def eigen_system(H):
    values, vectors = sparse.linalg.eigs(H,2,which='SR') #ARPACK!!
    energy_ground = values[0]
    return  vectors[:,0], energy_ground


init = 0.0
points = 1000  
final_value = 2*math.pi
steep = (final_value-init)/points
list_values_phase = np.arange(init,final_value,steep)
f1 = open("ground_state_energy.dat", "w")
for i in list_values_phase:
    phase = i
    f1.write(str(phase)+" ")
    H = np.asarray(tunneling(i))
    f1.write(str(np.real(eigen_system(H)[1]))+" ")
    f1.write("\n")
f1.close()



datalist = pylab.loadtxt("ground_state_energy.dat")
pylab.plot( datalist[:,0], datalist[:,1],label="ground state" )
pylab.legend()
pylab.xlabel("phase")
pylab.ylabel("Energy")
pylab.show()