def cij(i,j): # correlation between sites i,j pairs = [(2*i,2*j),(2*i+1,2*j),(2*i,2*j+1),(2*i+1,2*j+1)] # pairs = [(2*i,2*j),(2*i+1,2*j+1)] y1 = densitymatrix.restricted_dm(h,mode="KPM",pairs=pairs,npol=500) # y1 = densitymatrix.restricted_dm(h,mode="full",pairs=pairs,npol=500) # y1 = np.array(y1).reshape(2,2) # y1 = np.linalg.det(y1) # determinant # print(y1) # print(np.linalg.svd(y1,compute_uv=False)) # y2 = np.linalg.svd(y1,compute_uv=False) # print(np.sum(y2),np.sum(y1)) return np.sum(y1) # return correlation
def cij(i, j): # correlation between sites i,j
pairs = [(2 * i, 2 * j), (2 * i + 1, 2 * j), (2 * i, 2 * j + 1),
(2 * i + 1, 2 * j + 1)]
# pairs = [(2*i,2*j),(2*i+1,2*j+1)]
y1 = densitymatrix.restricted_dm(h, mode="KPM", pairs=pairs, npol=500)
# y1 = densitymatrix.restricted_dm(h,mode="full",pairs=pairs,npol=500)
# y1 = np.array(y1).reshape(2,2)
# y1 = np.linalg.det(y1) # determinant
# print(y1)
# print(np.linalg.svd(y1,compute_uv=False))
# y2 = np.linalg.svd(y1,compute_uv=False)
# print(np.sum(y2),np.sum(y1))
return np.sum(y1) # return correlation
g = geometry.chain()
g = g.supercell(100)
g.dimensionality = 0
h = g.get_hamiltonian()
#h.remove_spin()
#h.add_sublattice_imbalance(.5)
#h.shift_fermi(.5)
h.add_rashba(.5)
h.add_zeeman([0.,1.,0.])
#h.intra += np.diag(np.random.random(h.intra.shape[0]))
i = 20
j = 9
x = range(0,30)
pairs = [(i,i+k) for k in x] # create pairs
t1 = time.clock()
y1 = densitymatrix.restricted_dm(h,mode="KPM",pairs=pairs,npol=1000)
t2 = time.clock()
y2 = densitymatrix.restricted_dm(h,mode="full",pairs=pairs)
t3 = time.clock()
print(y1-y2)
print("Time KPM = ",t2-t1)
print("Time in inversion = ",t3-t2)
#print(np.trapz(y,x=x,dx=x[1]-x[0]))
plt.subplot(1,2,1)
plt.plot(x,y1.real,marker="o",label="KPM")
plt.plot(x,y2.real,marker="o",label="Green")
plt.legend()
plt.subplot(1,2,2)
plt.plot(x,y1.imag,marker="o",label="KPM")
plt.plot(x,y2.imag,marker="o",label="Green")
plt.legend()
# Add the root path of the pygra library import os import sys sys.path.append(os.path.dirname(os.path.realpath(__file__)) + "/../../../src") from pygra import geometry # library to create crystal geometries from pygra import hamiltonians # library to work with hamiltonians from pygra import sculpt # to modify the geometry from pygra import correlator from pygra import kpm from pygra import densitymatrix import numpy as np import matplotlib.pyplot as plt import time g = geometry.bichain() g = g.supercell(100) g.dimensionality = 0 h = g.get_hamiltonian(has_spin=False) h.add_sublattice_imbalance(.03) #h.add_rashba(.5) #h.add_zeeman([0.,1.,0.]) #h.intra += np.diag(np.random.random(h.intra.shape[0])) pairs = [(0, i) for i in range(20)] y1 = densitymatrix.restricted_dm(h, mode="KPM", pairs=pairs) y2 = densitymatrix.restricted_dm(h, mode="full", pairs=pairs) plt.scatter(range(20), y1, label="KPM", c="red", s=90, marker="o") plt.scatter(range(20), y2, label="Exact", c="blue", s=20, marker="o") plt.legend() plt.show()
import numpy as np
import matplotlib.pyplot as plt
import time
g = geometry.chain()
g = g.supercell(100)
g.dimensionality = 0
h = g.get_hamiltonian()
h.add_rashba(.5)
h.add_zeeman([0.,1.,0.])
h.intra += np.diag(np.random.random(h.intra.shape[0]))
i = 0
j = 9
t1 = time.clock()
rand = lambda : np.random.randint(0,40)
pairs = [(i,i+np.random.randint(1,8)) for i in range(10,20)]
y = densitymatrix.restricted_dm(h,mode="KPM",pairs=pairs)
t2 = time.clock()
y2 = densitymatrix.restricted_dm(h,mode="full",pairs=pairs)
t3 = time.clock()
print("Time KPM mode = ",t2-t1)
print("Time in full mode = ",t3-t2)
#print(np.trapz(y,x=x,dx=x[1]-x[0]))
plt.subplot(1,2,1)
x = range(len(y))
plt.plot(x,y.real,marker="o",label="KPM")
plt.plot(x,y2.real,marker="o",label="Green")
plt.legend()
plt.subplot(1,2,2)
plt.plot(x,y.imag,marker="o",label="KPM")
plt.plot(x,y2.imag,marker="o",label="Green")
plt.legend()
# Add the root path of the pygra library import os import sys sys.path.append(os.path.dirname(os.path.realpath(__file__)) + "/../../../src") from pygra import geometry from pygra import densitymatrix import numpy as np n = 400 g = geometry.chain(n) # chain g.dimensionality = 0 h = g.get_hamiltonian(has_spin=False) h.add_onsite(lambda r: 2.3 * np.cos(np.sqrt(2) / 2. * r[0])) pairs = [(n // 2, n // 2 + i) for i in range(n // 3)] y = densitymatrix.restricted_dm(h, mode="full", pairs=pairs).real import matplotlib.pyplot as plt x = np.array(range(len(y))) plt.plot(x, y * x) plt.show()
# Add the root path of the pygra library import os ; import sys ; sys.path.append(os.environ['PYGRAROOT']) from pygra import geometry from pygra import densitymatrix import numpy as np n = 400 g = geometry.chain(n) # chain g.dimensionality = 0 h = g.get_hamiltonian(has_spin=False) h.add_onsite(lambda r: 2.3*np.cos(np.sqrt(2)/2.*r[0])) pairs = [(n//2,n//2+i) for i in range(n//3)] y = densitymatrix.restricted_dm(h,mode="full",pairs=pairs).real import matplotlib.pyplot as plt x = np.array(range(len(y))) plt.plot(x,y*x) plt.show()