def Run_2(_T, _J, _i, _j, Phase, n=None):
'''
This func calculate the system with Inversion Symmetry, which means that for the upper half and the lower half, the spin terms change signs.
:para `n` defines how many layers (in upper half) contains the Spin term. In default, all of the upper half have the spin term.
'''
print("Start Calculation: Theta=%.3f , J=%.3f" % (_T, _J))
_S = np.zeros([N, 3])
layer = int(N/2) if n == None else min(int(n), int(N/2))
for i in range(layer):
_S[i, 0], _S[N-i-1, 0] = 1, -1
_S[i, 1], _S[N-i-1, 1] = _T, _T
# _S[N-i-1, 2] = np.pi
S = np.array([([s[0]*np.sin(s[1])*np.cos(s[2]), s[0] *
np.sin(s[1]) * np.sin(s[2]), s[0]*np.cos(s[1])])for s in _S])
# print(S)
h = Hamiltonian(N=N, J=_J, S=S)
res = TIC.Calc(h, CalcZ2=True, LogOut=False, settings=settings)
Phase[_i][_j] = TIC.TopoOrder(res)
# Phase[_i][_j] = _i*10+_j
# print("(", _i, ",", _j, "),", end="")
if Phase[_i][_j] != 0:
print("=========================================\nNon Trivial Phase!")
print("=========================================")
# sys.stderr.write("Theta=%.3f pi , J=%.3f, Result: C=%.4f , Z2=%s" %
# (_T/np.pi, _J, res.Chern, str(res._Z2)))
print("End Calculation: Theta=%.3f pi , J=%.3f, Result: C=%.4f , Z2=%s" %
(_T/np.pi, _J, res.Chern, str(res._Z2)))
return
def Run_0(_N, _J, _i, _j, Phase):
'''
This func calculate the system with uniform spin distribution in Z-direction.
'''
h = Hamiltonian(N=_N, J=_J)
res = TIC.Calc(h, CalcZ2=True, LogOut=False, settings=settings)
print(res.Chern)
Phase[_i][_j] = TIC.TopoOrder(res)
return
def Run_1(_N, _J, _i, _j, Phase):
'''
This func calculate the system with uniform spin distribution in Z-direction.
'''
print("Start Calc: N=%d, J=%.3f" % (int(_N), _J))
h = Hamiltonian(N=int(_N), J=_J, Delta=3.333, **CONST_HJZ)
res = Calc(h, CalcZ2=True, LogOut=False, settings=settings)
Phase[_i][_j] = TopoOrder(res)
print("End Calc: N=%d, J=%.3f; Res=%d" % (int(_N), _J, TopoOrder(res)))
return
def Run_SpinZ(_N, _J, _i, _j, Phase, Delta=3, CONST=CONST_HZL):
'''
This func calculate the system with uniform spin distribution in Z-direction.
Use default constants from Hai-Zhou Lu's paper.
'''
print("Start Calc: N=%d, J=%.3f" % (int(_N), _J))
h = Hamiltonian(N=int(_N), J=_J, Delta=Delta, **CONST)
res = Calc(h, CalcZ2=True, LogOut=False, settings=settings_strict)
Phase[_i][_j] = TopoOrder(res)
print("End Calc: N=%d, J=%.3f; Res=%d" % (int(_N), _J, TopoOrder(res)))
return
def CalcGap():
TEST_HJZ = {
"A1": 2.26,
"A2": 3.33,
"C": -0.0083,
"D1": 5.74,
"D2": 30.4,
"M": 0.28,
"B1": 6.86,
"B2": 44.5
}
TEST_HZL = { # Interesting!!!!!
"A1": 3.3,
"A2": 4.1,
"C": -0.0068,
"D1": 1.2,
"D2": -30.1,
"M": 0.28,
"B1": 1.5,
"B2": -54.1
}
N_min, N_max, Step, J = 10, 35, 5, 0.00
L = int((N_max - N_min) / Step + 1)
Gap = np.zeros([
L,
], dtype=float)
X = np.linspace(N_min, N_max, num=L, endpoint=True, dtype=int)
x = list(range(int(N_min / Step), int(N_max / Step + 1)))
for i in range(L):
# By Default it is Spin-Z
N = X[i]
h = Hamiltonian(N=N, J=J, Delta=1.9134, **TEST_HZL)
eig = np.array([x.real for x in (linalg.eig(h(0, 0))[0])])
eig.sort()
Gap[i] = eig[2 * N] - eig[2 * N - 1]
# print(Gap[i])
plt.subplot()
plt.plot(x, Gap, label=r"$\Delta_H$")
plt.scatter(x, Gap)
J = np.array(read3("PT_D1.9134_HZL_SpinZ18-09-05-08-46-02.txt")) * 2
plt.plot(x, J, color="red", label=r"$2\times J_c$")
plt.scatter(x, J, color="red", marker="^")
plt.legend(loc='upper right')
plt.xlabel(r"$Thickness (\rm QL)$")
plt.ylabel(r"$Gap(\rm eV)$")
plt.title(r"Critical $J$ & Hybridization Gap vs Thickness")
plt.savefig("Spin_Hybrid_vsThickness_10_35_D1.9134.png")
return
def PT_SpinZ(_N, _J_Max, _i, _j, Phase, _J_Min=0, _J_tol=1e-4, Delta=3.189, CONST=CONST_HZL, settings=settings):
assert _J_tol > 0, "_J_tol should >0!"
print("Start Calc: N=%d" % (int(_N)))
L, R = _J_Min, _J_Max
print("===>Calculate N=%d, J=%.3f" % (int(_N), L))
h = Hamiltonian(N=int(_N), J=L, Delta=Delta, **CONST)
res = Calc(h, CalcZ2=True, LogOut=False, settings=settings)
T_L = TopoOrder(res)
print("Calculate N=%d, J=%.3f" % (int(_N), R))
h = Hamiltonian(N=int(_N), J=R, Delta=Delta, **CONST)
res = Calc(h, CalcZ2=True, LogOut=False, settings=settings)
T_R = TopoOrder(res)
if T_L == T_R:
Phase[_i][_j] = -1
print("===>End Calc: N=%d. No phase transition, Res=%d" %
(int(_N), TopoOrder(res)))
else:
while (R-L) > _J_tol:
M = (R+L)/2
print("Calculate N=%d, J=%.3f" % (int(_N), M))
h = Hamiltonian(N=int(_N), J=M, Delta=Delta, **CONST)
res = Calc(h, CalcZ2=True, LogOut=False, settings=settings)
T_M = TopoOrder(res)
if T_M == T_R:
R = M
elif T_M == T_L:
L = M
else:
Phase[_i][_j] = R
raise Exception("Middle result different with either!")
Phase[_i][_j] = R
print("===>End Calc: N=%d, phase transition at %.3f" %
(int(_N), R))
return
def Run_HZL(_N, _J, _i, _j, Phase):
'''
This func calculate the system with uniform spin distribution in Z-direction.
Use the Parameters from the Hai-Zhou Lu's paper.
'''
print("Start Calc: N=%d, J=%.3f" % (int(_N), _J))
h = Hamiltonian(N=int(_N), J=_J, Delta=3.333, **CONST_HZL)
res = Calc(h, CalcZ2=True, LogOut=False, settings=settings)
Phase[_i][_j] = TopoOrder(res)
print("End Calc: N=%d, J=%.3f; Res=%d" % (int(_N), _J, TopoOrder(res)))
if TopoOrder(res) != 0:
stderr.write("!!!!!!!!\nN=%d, J=%.3f; Res=%d\n!!!!!!!!!!\n" %
(int(_N), _J, TopoOrder(res)))
return
def CalcGap():
N_min, N_max, J = 6, 30, 0.00
Gap = np.zeros([N_max + 1], dtype=float)
for N in range(N_min, N_max + 1):
h = Hamiltonian(N=N, J=J) # By Default it is Spin-Z
eig = np.array([x.real for x in (linalg.eig(h(0, 0))[0])])
eig.sort()
Gap[N] = eig[2 * N] - eig[2 * N - 1]
plt.subplot()
plt.plot(list(range(N_min, N_max + 1)), Gap[N_min:N_max + 1] * 1000)
plt.xlabel(r"$N$")
plt.ylabel(r"$Gap(\rm meV)$")
plt.title("Gap vs Thickness, No Spin")
plt.savefig("Gap_vs_Thickness_No_Spin.png")
return
def Run_Inv(_T, _J, _i, _j, Phase, N=20, n=None, Delta=3, CONST=CONST_HZL):
'''
This func calculate the system with Mirror Symmetry, which means that for the upper half and the lower half,the parallel components changes sign while the perpendicular term keep unchanged
:para `n` defines how many layers (in upper half) contains the Spin term. In default, all of the upper half have the spin term.
'''
print("Start Calculation: Theta=%.3f , J=%.3f" % (_T, _J))
_S = np.zeros([N, 3])
layer = int(N / 2) if n == None else min(int(n), int(N / 2))
for i in range(layer):
_S[i, 0], _S[N - i - 1, 0] = 1, 1
_S[i, 1], _S[N - i - 1, 1] = _T, _T
S = convertSpin(_S)
h = Hamiltonian(N=N, J=_J, S=S, Delta=Delta, **CONST)
res = Calc(h, CalcZ2=True, LogOut=False, settings=settings)
Phase[_i][_j] = TopoOrder(res)
print("End Calculation: Theta=%.3f pi , J=%.3f, Result: C=%.4f , Z2=%s" %
(_T / np.pi, _J, res.Chern, str(res._Z2)))
return
def Run_1(_N, _J, _i, _j, Phase):
'''
This func calculate the system with spin distribution: +z in the upper half and -z in the lower half.
If the # of layers is odd, then the layer in the very middle will have no spin to make sure the total spin in Z direction of this system to be ZERO.
'''
print("Start Calculation: N=%d , J=%.3f" % (_N, _J))
_S = np.zeros([_N, 3])
for i in range(int(_N / 2)):
_S[i, 0], _S[_N - i - 1, 0] = 1, -1
S = np.array([([
s[0] * np.sin(s[1]) * np.cos(s[2]), s[0] * np.sin(s[1]) * np.sin(s[2]),
s[0] * np.cos(s[1])
]) for s in _S])
h = Hamiltonian(N=_N, J=_J, S=S)
res = TIC.Calc(h, CalcZ2=True, LogOut=False, settings=settings)
Phase[_i][_j] = TIC.TopoOrder(res)
print("End Calculation: N=%d , J=%.3f, Result: C=%.4f , Z2=%s" %
(_N, _J, res.Chern, str(res._Z2)))
# Phase[_i][_j] = _i*10+_j
return
def Run_4(_N, _J, _i, _j, Phase, n=1):
r'''
This func calculate the system with spin distribution: +z in the first $n$ layer and the last $n$ layer.
'''
print("Start Calculation: N=%d , J=%.3f" % (_N, _J))
_S = np.zeros([_N, 3])
assert n <= int(_N / 2), "n should be less than half of the layer #。"
for i in range(n):
_S[i, 0], _S[_N - i - 1, 0] = 1, 1
S = np.array([([
s[0] * np.sin(s[1]) * np.cos(s[2]), s[0] * np.sin(s[1]) * np.sin(s[2]),
s[0] * np.cos(s[1])
]) for s in _S])
# print(S)
h = Hamiltonian(N=_N, J=_J, S=S)
res = TIC.Calc(h, CalcZ2=True, LogOut=False, settings=settings)
Phase[_i][_j] = TIC.TopoOrder(res)
print("End Calculation: N=%d , J=%.3f, Result: C=%.4f , Z2=%s" %
(_N, _J, res.Chern, str(res._Z2)))
return
def Run_5(_N, _J, _i, _j, Phase):
'''
This func calculate the system with uniform spin distribution in Z-direction.
'''
print("Start Calculation: N=%d , J=%.3f" % (_N, _J))
_S = np.zeros([_N, 3])
for i in range(_N):
_S[i, 0] = 1
_S[i, 1] = np.pi / 2
S = np.array([([
s[0] * np.sin(s[1]) * np.cos(s[2]), s[0] * np.sin(s[1]) * np.sin(s[2]),
s[0] * np.cos(s[1])
]) for s in _S])
# print(S)
h = Hamiltonian(N=_N, J=_J, S=S)
res = TIC.Calc(h, CalcZ2=True, LogOut=False, settings=settings)
Phase[_i][_j] = TIC.TopoOrder(res)
print("End Calculation: N=%d , J=%.3f, Result: C=%.4f , Z2=%s" %
(_N, _J, res.Chern, str(res._Z2)))
# Phase[_i][_j] = _i*10+_j
return
z2pack.plot.wcc(result, axis=ax)
plt.savefig("TestWCC_Alone_Z-Spin.png")
if __name__ == "__main__":
N, J = 20, 0.00
S_ = np.zeros([N, 3])
# S_[0, 0], S_[-1, 0] = 1, 1
# S_[1, 0], S_[-2, 0] = 1, 1
# S_[2, 0], S_[-3, 0] = 1, 1
layer = int(N/2)
_S = np.zeros([N, 3])
for i in range(layer):
_S[i, 0], _S[N-i-1, 0] = 1, 1
_S[i, 1], _S[N-i-1, 1] = 0.47124, 0.47124
_S[N-i-1, 2] = np.pi
S = np.array([([s[0]*np.sin(s[1])*np.cos(s[2]), s[0]*np.sin(s[1])
* np.sin(s[2]), s[0]*np.cos(s[1])])for s in S_])
print(S)
h = Hamiltonian(N=N, J=J)
from TI_Film import plotLine
plotLine(h, 2*N-2, 2*N+2)
# e = Eig(h)
# plotBS(e, 2*N-2, 2*N+2, title="TI Film: z&-z in 3 layers, J=0.01, 4 bands")
# h = Ham_Small(0.02, 0.02)
# bands=[2*N-2, 2*N],
# res = Calc(h, KScale=1, CalcZ2=False, LogOut=True)
# # print("Chern=", res.Chern)
# res.plotChern()
import numpy as np
# import matplotlib as mpl
# # mpl.use("Agg")
# from matplotlib import pyplot as plt
from PhaseDiagram import PhaseDiag
from _utils import nt, convertSpin, settings, settings_strict, CONST_HJZ, CONST_HZL
from TI_Film import Hamiltonian, plotLine
from TopoInvCalc import Calc, TopoOrder
if __name__ == '__main__':
N, J = 25, 0.00
h = Hamiltonian(N=N, J=J, Delta=1.9134, **CONST_HZL)
res = Calc(h, CalcZ2=False, KScale=2, settings=settings_strict)
res.plotChern(title="N=25 (5 QLs), J=0.00 eV, Spin-Z",
filename="HZL_25_0.00_1.9134_K2")
# xRange, yRange, Nx, Ny = 0.05, 0.05, 50, 50
# plotLine(h, 2*N-4, 2*N+4, xRange=xRange, Nx=Nx,
# title="Band Structure(8 bands), N=30, Delta=$1.9134\AA$, No Spin\nParameters from Hai-Zhou Lu's paper.", filename="N30_J0_D1.9134")
def is_Chern(J0, c_tol=0.1):
h = Hamiltonian(N=N, J=J0, S=S)
res = TIC.Calc(h, CalcZ2=False)
return abs(res.Chern) > c_tol
