def generateParticleForABFrequency():
"""
This function generates the R function for four different voltages, as a
function of a changing edge. All other parameters are fixed. The result
is used for th Fourier Analysis of the AB oscillations at different voltages.
"""
Vpoints = np.array([mpf(i)/mpf(10**6) for i in [10, 20, 30, 40]])
Nterms= 201
dist1 = np.array([mpf('2.5')/ mpf(10**(6))]*Nterms)
dist2 = np.linspace(mpf('2.0')/mpf(10**(6)), mpf('3.0')/mpf(10**(6)), Nterms)
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(9,2),(9,2),(5,2),(5,2)]],
"c":[1,1,1,1],
"g":[1/mpf(8), 1/mpf(8), 1/mpf(8), 1/mpf(8)],
"x":[-dist1, dist2, -dist1, dist2]}
mp.mp.dps= 150
A = base_parameters(genData, V = Vpoints, Q = 1/mpf(4), T = 0)
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 550)
B.genAnswer()
return A, B, dist2
def Propagator_three_modes(saving=False):
"""Plots the modulating function and interference current for an edge with
3 modes."""
Vpoints = mp.linspace(0, mpf('1.') / mpf(10**4), 201)
dist1 = np.array(mpf('4.5') / mpf(10**(6)))
genData = {
"v": [mpf(i) * mpf(10**j) for (i, j) in [(10, 3), (3, 3), (5, 3)]],
"x": [dist1, dist1, dist1],
"g": [mpf(1) / mpf(10),
mpf(1) / mpf(10),
mpf(1) / mpf(10)],
"c": [1, 1, 1]
}
mp.mp.dps = 50
A = base_parameters(genData,
V=Vpoints,
Q=1 / mpf(4),
T=mpf(5) / mpf(10**3))
B = Rfunc_constructor(A, method='series')
B.setParameter(nterms=800)
_, interference = Current(B)
fig = plt.figure()
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax = fig.add_subplot(211)
ax.plot(Vpoints, interference, label=r"With interference", linewidth=1.5)
for i in ax.get_lines():
i.set_color('black')
ax.set_title(r'Tunnelling current for edge with three modes')
ax.set_ylabel(r"$I_B/\mathrm{max}(I_B){}$")
ax.set_ybound([0, 1])
ax.set_yticks([0, .25, .5, .75, 1])
ax.set_yticklabels([0, 0.25, 0.5, 0.75, 1])
ax.set_xticks(xt)
ax.set_xticklabels([])
ax.legend(loc='upper right', prop={'size': 12})
plt.setp(ax.get_xticklabels(), fontsize=12.)
plt.setp(ax.get_yticklabels(), fontsize=12.)
ax.grid(True)
ax2 = fig.add_subplot(212)
ax2.plot(Vpoints, B.rrfunction, linewidth=1.5)
ax2.get_lines()[0].set_color('black')
ax2.set_title(r'Modulating function for edge with three modes')
ax2.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$")
ax2.set_xlabel(r'Volt [$\mu$V]')
ax2.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax2.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
ax2.set_xticks(xt)
ax2.set_xticklabels(xt_labels)
ax2.grid(True)
plt.setp(ax2.get_xticklabels(), fontsize=12.)
plt.setp(ax2.get_yticklabels(), fontsize=12.)
if saving: plt.savefig('multi_mode_error.pdf', bbox_inches=0, dpi=300)
plt.show()
return B
def generateParticleForABFrequency():
"""
This function generates the R function for four different voltages, as a
function of a changing edge. All other parameters are fixed. The result
is used for th Fourier Analysis of the AB oscillations at different voltages.
"""
Vpoints = np.array([mpf(i) / mpf(10**6) for i in [10, 20, 30, 40]])
Nterms = 201
dist1 = np.array([mpf('2.5') / mpf(10**(6))] * Nterms)
dist2 = np.linspace(
mpf('2.0') / mpf(10**(6)),
mpf('3.0') / mpf(10**(6)), Nterms)
genData = {
"v":
[mpf(i) * mpf(10**j) for (i, j) in [(9, 2), (9, 2), (5, 2), (5, 2)]],
"c": [1, 1, 1, 1],
"g": [1 / mpf(8), 1 / mpf(8), 1 / mpf(8), 1 / mpf(8)],
"x": [-dist1, dist2, -dist1, dist2]
}
mp.mp.dps = 150
A = base_parameters(genData, V=Vpoints, Q=1 / mpf(4), T=0)
B = Rfunc_constructor(A, method='series')
B.setParameter(nterms=550)
B.genAnswer()
return A, B, dist2
def main_plot(saving = False):
"""Main plot:
Plots the mod-H function, the current with and without interference
# and transmission"""
Vpoints = mp.linspace(0, mpf('1.')/mpf(10**4), 201)
dist1 = mpf('2.0')/ mpf(10**(6))
dist2 = mpf('1.8')/mpf(10**(6))
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(7,3),(7,3),(1,3),(1,3)]],
"c":[1,1,1,1],
"g":[mpf(1)/mpf(8),mpf(1)/mpf(8),mpf(1)/mpf(8),mpf(1)/mpf(8)],
"x":[-dist1, dist2, -dist1, dist2]}
mp.mp.dps= 60
A = base_parameters(genData, V = Vpoints, Q = 1/mpf(4), T = 1/mpf(10**4))
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 450, maxA = 11, maxK = 11)
single, interference = Current(B)
fig = plt.figure()
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax = fig.add_subplot(211)
ax.plot(Vpoints,interference/np.max(single), label = r"With interference", linewidth=1.5)
ax.plot(Vpoints,single/np.max(single), label = r"Without interference", linewidth=1.5)
ax.get_lines()[1].set_dashes([5,2])
for i in ax.get_lines(): i.set_color('black')
ax.set_title(r'Tunnelling current for the Pfaffian state', fontsize=16)
ax.set_ylabel(r"$I_B/\mathrm{max}(I_B){}$", fontsize=16)
ax.set_ybound([0,1])
ax.set_yticks([.25, .5, .75, 1])
ax.set_yticklabels([0.25, 0.5, 0.75, 1])
ax.set_xticks(xt)
ax.set_xticklabels([])
ax.legend(loc = 'upper right', prop={'size':14})
plt.setp(ax.get_xticklabels(), fontsize = 14)
plt.setp(ax.get_yticklabels(), fontsize = 14)
ax.grid(True)
ax2 = fig.add_subplot(212)
ax2.plot(Vpoints, B.rrfunction, linewidth=1.5)
ax2.get_lines()[0].set_color('black')
ax2.set_title(r'Modulating function for the Pfaffian state', fontsize=16)
ax2.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax2.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax2.xaxis.set_label_coords(.9, -0.12)
ax2.set_yticks([-0.25,0,.25,.5,.75,1])
ax2.set_yticklabels([-0.25,0,0.25,0.5,0.75,1])
ax2.set_xticks(xt)
ax2.set_xticklabels(xt_labels)
ax2.grid(True)
plt.setp(ax2.get_xticklabels(), fontsize=14)
plt.setp(ax2.get_yticklabels(), fontsize=14)
if saving: plt.savefig('main_plot.pdf', bbox_inches=0, dpi=300)
plt.subplots_adjust(hspace=0.3)
plt.show()
return B
def temperature(saving=False):
Vpoints = mp.linspace(0, mpf('1.') / mpf(10**4), 201)
dist1 = np.array(mpf('3.5') / mpf(10**(6)))
dist2 = np.array(mpf('3.5') / mpf(10**(6)))
genData = {
"v":
[mpf(i) * mpf(10**j) for (i, j) in [(9, 4), (9, 4), (9, 3), (9, 3)]],
"c": [1, 1, 1, 1],
"g": [1 / mpf(8), 1 / mpf(8), 1 / mpf(8), 1 / mpf(8)],
"x": [-dist1, dist2, -dist1, dist2]
}
names = [0, 10, 18]
temperatureset = [mpf(i) / mpf(10**3) for i in names]
ans = []
fig = plt.figure()
ax = fig.add_subplot(111)
for i, j in enumerate(temperatureset):
A = base_parameters(genData, V=Vpoints, Q=1 / mpf(4), T=j)
if j < 9 / mpf(10**3):
mp.mp.dps = 30
B = Rfunc_constructor(A, method='series')
B.setParameter(nterms=500, maxA=15, maxK=15)
else:
mp.mp.dps = 20
B = Rfunc_constructor(A, method='fortran')
B.setParameter(nterms=2 * 132000, maxA=25, maxK=25)
B.genAnswer()
ans.append(B)
ax.plot(Vpoints, B.rrfunction, \
label = str(names[i]) +' [mK]', linewidth=1.5)
dashstyle = [(None, None), [7, 2], [3, 4]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_title(
r'The modulating function \\ for different temperature scales',
fontsize=16)
ax.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax.xaxis.set_label_coords(.9, -0.06)
ax.set_ybound([-.25, 1.125])
ax.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.grid(True)
ax.legend(loc='upper right', prop={'size': 14})
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
if saving: plt.savefig('temperature.pdf', bbox_inches=0, dpi=300)
plt.show()
return ans
def multi_modes(saving = False):
"""Plots the modulating function and interference current for an edge with
3 modes."""
Vpoints = mp.linspace(0, mpf('2.')/mpf(10**4), 201)
dist1 = np.array(mpf('4.5')/ mpf(10**(6)))
dist2 = np.array(mpf('3.')/mpf(10**(6)))
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(10,3),(10,3),(3,3),(3,3),(5,3),(5,3)]],
"x":[dist1, -dist2, dist1, -dist2,dist1, -dist2],
"g":[mpf(1)/mpf(10), mpf(1)/mpf(10), mpf(1)/mpf(10), mpf(1)/mpf(10),mpf(1)/mpf(10), mpf(1)/mpf(10)],
"c":[1,1,1,1,1,1]}
mp.mp.dps= 90
A = base_parameters(genData, V = Vpoints, Q = 1/mpf(4), T = mpf(0))
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 800)
single, interference = Current(B)
fig = plt.figure()
xt = np.linspace(0, 2 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax = fig.add_subplot(211)
ax.plot(Vpoints,interference/np.max(single), label = r"With interference", linewidth=1.5)
ax.plot(Vpoints,single/np.max(single), label = r"With interference", linewidth=1.5)
ax.get_lines()[1].set_dashes([5,2])
for i in ax.get_lines(): i.set_color('black')
ax.set_title(r'Tunnelling current for edge with three modes')
ax.set_ylabel(r"$I_B/\mathrm{max}(I_B){}$")
ax.set_ybound([0,1])
ax.set_yticks([0,.25, .5, .75, 1])
ax.set_yticklabels([0,0.25, 0.5, 0.75, 1])
ax.set_xticks(xt)
ax.set_xticklabels([])
ax.legend(loc = 'upper right', prop={'size':14})
plt.setp(ax.get_xticklabels(), fontsize = 14)
plt.setp(ax.get_yticklabels(), fontsize = 14)
ax.grid(True)
ax2 = fig.add_subplot(212)
ax2.plot(Vpoints, B.rrfunction, linewidth=1.5)
ax2.get_lines()[0].set_color('black')
ax2.set_title(r'Modulating function for edge with three modes', fontsize=16)
ax2.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax2.set_xlabel(r'Volt [$\mu$V]')
ax2.set_yticks([-0.25,0,.25,.5,.75,1])
ax2.set_yticklabels([-0.25,0,0.25,0.5,0.75,1])
ax2.set_xticks(xt)
ax2.set_xticklabels(xt_labels)
ax2.grid(True)
plt.setp(ax2.get_xticklabels(), fontsize=12.)
plt.setp(ax2.get_yticklabels(), fontsize=12.)
if saving: plt.savefig('main_plot.pdf', bbox_inches=0, dpi=300)
plt.show()
return B
def temperature(saving = False):
Vpoints = mp.linspace(0, mpf('1.')/mpf(10**4), 201)
dist1 = np.array(mpf('3.5')/ mpf(10**(6)))
dist2 = np.array(mpf('3.5')/mpf(10**(6)))
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(9,4),(9,4),(9,3),(9,3)]],
"c":[1,1,1,1],
"g":[1/mpf(8), 1/mpf(8), 1/mpf(8), 1/mpf(8)],
"x":[-dist1, dist2, -dist1, dist2]}
names = [0,10,18]
temperatureset = [mpf(i)/mpf(10**3) for i in names]
ans = []
fig = plt.figure()
ax = fig.add_subplot(111)
for i, j in enumerate(temperatureset):
A = base_parameters(genData, V = Vpoints, Q = 1/mpf(4), T = j)
if j < 9/mpf(10**3):
mp.mp.dps = 30
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 500, maxA = 15, maxK = 15)
else:
mp.mp.dps = 20
B = Rfunc_constructor(A, method = 'fortran')
B.setParameter(nterms = 2*132000, maxA = 25, maxK = 25)
B.genAnswer()
ans.append(B)
ax.plot(Vpoints, B.rrfunction, \
label = str(names[i]) +' [mK]', linewidth=1.5)
dashstyle = [(None, None), [7,2], [3,4]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_title(r'The modulating function \\ for different temperature scales', fontsize=16)
ax.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax.xaxis.set_label_coords(.9, -0.06)
ax.set_ybound([-.25,1.125])
ax.set_yticks([-0.25,0,.25,.5,.75,1])
ax.set_yticklabels([-0.25,0,0.25,0.5,0.75,1])
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.grid(True)
ax.legend(loc='upper right', prop={'size':14})
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
if saving: plt.savefig('temperature.pdf', bbox_inches=0, dpi=300)
plt.show()
return ans
def distanceChangeParticleForAB(strong_effect = True, abelian = False):
"""
Computes modulating function as a function of changing the distance along
one edge.
Warning: this function can take very long to complete.
"""
assert isinstance(strong_effect, bool)
Vpoints = np.array([mpf(50)/mpf(10**6)])
Nterms= 201
dist1 = np.array([mpf('2.5')/ mpf(10**(6))]*Nterms)
if strong_effect:
dist2 = np.linspace(mpf('2.0')/mpf(10**(6)), mpf('3.0')/mpf(10**(6)), Nterms)
else:
dist2 = np.linspace(mpf('2.25')/mpf(10**(6)), mpf('2.75')/mpf(10**(6)),
Nterms)
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(9,2),(9,2),(6,2),(6,2)]],
"c":[1,1,1,1],
"g":[mpf(1)/mpf(10),mpf(1)/mpf(10),mpf(1)/mpf(8),mpf(1)/mpf(8)],
"x":[-dist1, dist2, -dist1, dist2]}
Qe = 1/mpf(4)
if not strong_effect:
genData["v"] = [mpf(i) * mpf(10**j) for (i,j) in [(8,3),(8,3),(3,3),(3,3)]]
# Abelian case is not used in text
if abelian:
Qe = 1/mpf(2)
genData["c"] = [1,1]
genData["g"] = [1/mpf(2), 1/mpf(2)]
genData["x"] = [-dist1, dist2]
if strong_effect:
genData["v"] = [mpf(i) * mpf(10**j) for (i,j) in [(5,2),(5,2)]]
else:
genData["v"] = [mpf(i) * mpf(10**j) for (i,j) in [(5,3),(5,3)]]
mp.mp.dps= 150
A = base_parameters(genData, V = Vpoints, Q = Qe, T = 0)
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 500, maxA = 20, maxK = 20)
B.genAnswer()
return A,B, dist2
def distanceChangeParticle():
"""
Computes modulating function as a function of changing the distance along
one edge.
Warning: this function can take very long to complete.
"""
Vpoints = np.array([mpf(60)/mpf(10**6)])
Nterms= 201
dist1 = np.array([mpf('2.5')/ mpf(10**(6))]*Nterms)
dist2 = np.linspace(mpf('0.001')/mpf(10**(6)), mpf('3.0')/mpf(10**(6)), Nterms)
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(1,3),(1,3),(6,2),(6,2)]],
"c":[1,1,1,1],
"g":[mpf(1)/mpf(8),mpf(1)/mpf(8),mpf(1)/mpf(8),mpf(1)/mpf(8)],
"x":[-dist1, dist2, -dist1, dist2]}
mp.mp.dps= 150
A = base_parameters(genData, V = Vpoints, Q = 1/mpf(4), T = 0)
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 700)
B.genAnswer()
return A,B
def particles_12_5(saving=False):
Vpoints = mp.linspace(0, mpf('1.') / mpf(10**4), 201)
dist1 = mpf('2.4') / mpf(10**(6))
dist2 = mpf('2.1') / mpf(10**(6))
genData = {
"v": [
mpf(i) * mpf(10**j)
for (i, j) in [(5, 3), (5, 3), (1.4, 3), (1.4, 3)]
],
"x": [-dist1, dist2, -dist1, dist2]
}
LaughlinE5 = {
"g": [mpf(2) / mpf(5), mpf(2) / mpf(5)],
"c": [1, 1],
"x": [-dist1, dist2],
"v": [mpf(i) * mpf(10**j) for (i, j) in [(5, 3), (5, 3)]],
"Q": 1 / mpf(3)
}
BS25 = {
"g":
[mpf(1) / mpf(10),
mpf(1) / mpf(10),
mpf(1) / mpf(8),
mpf(1) / mpf(8)],
"c": [1, 1, 1, 1],
"Q": 1 / mpf(5)
}
HH25 = {
"g":
[mpf(1) / mpf(5),
mpf(1) / mpf(5),
mpf(2) / mpf(5),
mpf(2) / mpf(5)],
"c": [1, 1, 1, 1],
"Q": 1 / mpf(5)
}
aRR3 = {
"g": [
mpf(1) / mpf(10),
mpf(1) / mpf(10),
mpf(3) / mpf(10),
mpf(3) / mpf(10)
],
"c": [1, 1, -1, -1],
"Q":
mpf(1) / mpf(5)
}
particleset = [HH25, aRR3, BS25, LaughlinE5]
names = [
r"$\mathrm{HH}_{2/5}$ (e/5)", r"$\overline{\mathrm{RR}}_{k=3} $ (e/5)",
r"$\mathrm{BS}_{2/5}$ (e/5)", r"Laughlin (2e/5)"
]
mp.mp.dps = 60
fig = plt.figure()
ax = fig.add_subplot(111)
ans = []
for i in range(len(names)):
particle = genData.copy()
particle.update(particleset[i])
Qe = particle["Q"]
del particle["Q"]
A = base_parameters(particle, V=Vpoints, Q=Qe, T=1 / mpf(10**3))
B = Rfunc_constructor(A, method='series')
B.setParameter(nterms=1000, maxA=12, maxK=12)
B.genAnswer()
ans.append(B)
ax.plot(Vpoints, B.rrfunction, label=names[i], linewidth=1.5)
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
dashstyle = [(None, None), [10, 4], [6, 3, 1, 3, 1, 3], [2, 2], [2, 6]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
ax.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax.xaxis.set_label_coords(.9, -0.06)
ax.set_ybound([-.5, 1])
ax.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.set_title(r"Modulating function for $\nu = 12/5 $ candidates",
fontsize=16)
ax.legend(loc='upper right', prop={'size': 14})
ax.grid(True)
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
if saving: plt.savefig('particles_12_5.pdf', bbox_inches=0, dpi=300)
plt.show()
return ans
def main_plot(saving=False):
"""Main plot:
Plots the mod-H function, the current with and without interference
# and transmission"""
Vpoints = mp.linspace(0, mpf('1.') / mpf(10**4), 201)
dist1 = mpf('2.0') / mpf(10**(6))
dist2 = mpf('1.8') / mpf(10**(6))
genData = {
"v":
[mpf(i) * mpf(10**j) for (i, j) in [(7, 3), (7, 3), (1, 3), (1, 3)]],
"c": [1, 1, 1, 1],
"g":
[mpf(1) / mpf(8),
mpf(1) / mpf(8),
mpf(1) / mpf(8),
mpf(1) / mpf(8)],
"x": [-dist1, dist2, -dist1, dist2]
}
mp.mp.dps = 60
A = base_parameters(genData, V=Vpoints, Q=1 / mpf(4), T=1 / mpf(10**4))
B = Rfunc_constructor(A, method='series')
B.setParameter(nterms=450, maxA=11, maxK=11)
single, interference = Current(B)
fig = plt.figure()
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax = fig.add_subplot(211)
ax.plot(Vpoints,
interference / np.max(single),
label=r"With interference",
linewidth=1.5)
ax.plot(Vpoints,
single / np.max(single),
label=r"Without interference",
linewidth=1.5)
ax.get_lines()[1].set_dashes([5, 2])
for i in ax.get_lines():
i.set_color('black')
ax.set_title(r'Tunnelling current for the Pfaffian state', fontsize=16)
ax.set_ylabel(r"$I_B/\mathrm{max}(I_B){}$", fontsize=16)
ax.set_ybound([0, 1])
ax.set_yticks([.25, .5, .75, 1])
ax.set_yticklabels([0.25, 0.5, 0.75, 1])
ax.set_xticks(xt)
ax.set_xticklabels([])
ax.legend(loc='upper right', prop={'size': 14})
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
ax.grid(True)
ax2 = fig.add_subplot(212)
ax2.plot(Vpoints, B.rrfunction, linewidth=1.5)
ax2.get_lines()[0].set_color('black')
ax2.set_title(r'Modulating function for the Pfaffian state', fontsize=16)
ax2.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax2.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax2.xaxis.set_label_coords(.9, -0.12)
ax2.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax2.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
ax2.set_xticks(xt)
ax2.set_xticklabels(xt_labels)
ax2.grid(True)
plt.setp(ax2.get_xticklabels(), fontsize=14)
plt.setp(ax2.get_yticklabels(), fontsize=14)
if saving: plt.savefig('main_plot.pdf', bbox_inches=0, dpi=300)
plt.subplots_adjust(hspace=0.3)
plt.show()
return B
def particles_5_2(saving=False):
Vpoints = mp.linspace(0, mpf('1.') / mpf(10**4), 201)
dist1 = mpf('2.4') / mpf(10**(6))
dist2 = mpf('2.1') / mpf(10**(6))
genData = {
"v": [
mpf(i) * mpf(10**j)
for (i, j) in [(5, 3), (5, 3), (1.4, 3), (1.4, 3)]
],
"x": [-dist1, dist2, -dist1, dist2]
}
pfaffE2 = {
"g": [mpf(1) / mpf(2), mpf(1) / mpf(2)],
"c": [1, 1],
"x": [-dist1, dist2],
"v": [mpf(i) * mpf(10**j) for (i, j) in [(5, 3), (5, 3)]],
"Q": 1 / mpf(2)
}
pfaff = {
"g":
[mpf(1) / mpf(8),
mpf(1) / mpf(8),
mpf(1) / mpf(8),
mpf(1) / mpf(8)],
"c": [1, 1, 1, 1],
"Q": 1 / mpf(4)
}
apf = {
"g":
[mpf(1) / mpf(8),
mpf(1) / mpf(8),
mpf(3) / mpf(8),
mpf(3) / mpf(8)],
"c": [1, 1, -1, -1],
"Q": 1 / mpf(4)
}
state331 = {
"g":
[mpf(1) / mpf(8),
mpf(1) / mpf(8),
mpf(1) / mpf(4),
mpf(1) / mpf(4)],
"c": [1, 1, 1, 1],
"Q": 1 / mpf(4)
}
particleset = [apf, state331, pfaff, pfaffE2]
names = [
"Anti-Pfaffian (e/4)", "(3,3,1)-state (e/4)", "Pfaffian (e/4)",
"Laughlin (e/2)"
]
mp.mp.dps = 60
fig = plt.figure()
ax = fig.add_subplot(111)
ans = []
for i in range(0, 4):
particle = genData.copy()
particle.update(particleset[i])
Qe = particle["Q"]
del particle["Q"]
A = base_parameters(particle, V=Vpoints, Q=Qe, T=1 / mpf(10**3))
B = Rfunc_constructor(A, method='series')
B.setParameter(nterms=1200, maxA=12, maxK=12)
B.genAnswer()
### uncomment to return all instances
# ans.extend([copy.deepcopy(A),copy.deepcopy(B)])
###
if B.rrfunction.shape[1] > 1:
ax.plot(Vpoints, B.rrfunction[:, 0], label=names[i], linewidth=1.5)
else:
ax.plot(Vpoints, B.rrfunction, label=names[i], linewidth=1.5)
dashstyle = [(None, None), [10, 4], [5, 3, 1, 3], [2, 4]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
ax.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax.xaxis.set_label_coords(.9, -0.06)
ax.set_ybound([-.5, 1])
ax.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.set_title(r"Modulating function for $\nu = 5/2 $ candidates",
fontsize=16)
ax.legend(loc='upper right', prop={'size': 14})
ax.grid(True)
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
if saving: plt.savefig('particles_5_2.pdf', bbox_inches=0, dpi=300)
plt.show()
return ans
def frequencyParticle(plotting=True):
"""This function constructs and computes the modulating functions,
which will be used in the frequency analysis
It comes with an optional plotting instruction -- this was used to look for
a "nice" parameter set.
"""
# Voltages array and distances.
Vpoints = mp.linspace(0, mpf('1.') / mpf(10**4), 201)
dist1 = np.array(mpf('4.0') / mpf(10**(6)))
dist2 = np.array(mpf('2.5') / mpf(10**(6)))
# We did not have a particular anyon in mind -- frequency is
# independent of the g-values anyway.
particletype = { \
"g":[mpf(1)/mpf(8), mpf(1)/mpf(8), mpf(1)/mpf(6), mpf(1)/mpf(6)],
"c":[1,1,1,1],
"v":[mpf(i) * mpf(10**j) for (i,j) in [(3,3),(3,3),(9,2),(9,2)]],
"x":[-dist1, dist2, -dist1, dist2],
"Q":1/mpf(4)}
particleset = [particletype]
if plotting:
# plotting is optional
fig = plt.figure()
ax = fig.add_subplot(111)
# we can add more particle types to particleset, and loop over these
for particle in particleset:
Qe = particle["Q"]
del particle["Q"]
# because of the large range of the voltage and low values of the
# velocities we enable many oscillations in the spectrum
# The downside is that we require an insane precision (170 digits)
mp.mp.dps = 170
# The T=0 function behaves requires high precision numbers.
# At finite temperatures we run into two problems:
# (1) Need high precision numbers
# (2) Need large number of terms
# We can only fix one of these at a time -- the fortran + cnct method
# can handle (to some extent) the large number of terms, but does not
# support arbitrary precision
# Conclusion: stick to T=0 and you only encounter problems with
# lack of high-precision numbers
A = base_parameters(particle, V=Vpoints, Q=Qe, T=0)
B = Rfunc_constructor(A, method='series')
B.setParameter(nterms=1000)
B.genAnswer()
# fix this output if you are looking at multiple particle species
ans = [A, B]
if plotting:
ax.plot(Vpoints, B.rrfunction, linewidth=1.5)
particle["Q"] = Qe
# plotting instructions. Dashstyle will give problems for more than
# 3 particles -- just add more styles.
if plotting:
dashstyle = [(None, None), [7, 2], [3, 4]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_ylabel(r"H_mod")
ax.set_xlabel(r'Volt')
ax.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.grid(True)
plt.setp(ax.get_xticklabels(), fontsize=12.)
plt.setp(ax.get_yticklabels(), fontsize=12.)
plt.show()
return ans
def frequencyParticle(plotting = True):
"""This function constructs and computes the modulating functions,
which will be used in the frequency analysis
It comes with an optional plotting instruction -- this was used to look for
a "nice" parameter set.
"""
# Voltages array and distances.
Vpoints = mp.linspace(0, mpf('1.')/mpf(10**4), 201)
dist1 = np.array(mpf('4.0')/ mpf(10**(6)))
dist2 = np.array(mpf('2.5')/mpf(10**(6)))
# We did not have a particular anyon in mind -- frequency is
# independent of the g-values anyway.
particletype = { \
"g":[mpf(1)/mpf(8), mpf(1)/mpf(8), mpf(1)/mpf(6), mpf(1)/mpf(6)],
"c":[1,1,1,1],
"v":[mpf(i) * mpf(10**j) for (i,j) in [(3,3),(3,3),(9,2),(9,2)]],
"x":[-dist1, dist2, -dist1, dist2],
"Q":1/mpf(4)}
particleset = [particletype]
if plotting:
# plotting is optional
fig = plt.figure()
ax = fig.add_subplot(111)
# we can add more particle types to particleset, and loop over these
for particle in particleset:
Qe = particle["Q"]
del particle["Q"]
# because of the large range of the voltage and low values of the
# velocities we enable many oscillations in the spectrum
# The downside is that we require an insane precision (170 digits)
mp.mp.dps= 170
# The T=0 function behaves requires high precision numbers.
# At finite temperatures we run into two problems:
# (1) Need high precision numbers
# (2) Need large number of terms
# We can only fix one of these at a time -- the fortran + cnct method
# can handle (to some extent) the large number of terms, but does not
# support arbitrary precision
# Conclusion: stick to T=0 and you only encounter problems with
# lack of high-precision numbers
A = base_parameters(particle, V = Vpoints, Q = Qe, T = 0)
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 1000)
B.genAnswer()
# fix this output if you are looking at multiple particle species
ans = [A,B]
if plotting:
ax.plot(Vpoints, B.rrfunction, linewidth=1.5)
particle["Q"] = Qe
# plotting instructions. Dashstyle will give problems for more than
# 3 particles -- just add more styles.
if plotting:
dashstyle = [(None, None), [7,2], [3,4]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_ylabel(r"H_mod")
ax.set_xlabel(r'Volt')
ax.set_yticks([-0.25,0,.25,.5,.75,1])
ax.set_yticklabels([-0.25,0,0.25,0.5,0.75,1])
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.grid(True)
plt.setp(ax.get_xticklabels(), fontsize=12.)
plt.setp(ax.get_yticklabels(), fontsize=12.)
plt.show()
return ans
def particles_12_5(saving = False):
Vpoints = mp.linspace(0, mpf('1.')/mpf(10**4), 201)
dist1 = mpf('2.4')/ mpf(10**(6))
dist2 = mpf('2.1')/mpf(10**(6))
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(5,3),(5,3),(1.4,3),(1.4,3)]],
"x":[-dist1, dist2, -dist1, dist2]}
LaughlinE5 = {
"g":[mpf(2)/mpf(5),mpf(2)/mpf(5)],
"c":[1,1],
"x":[-dist1, dist2],
"v":[mpf(i) * mpf(10**j) for (i,j) in [(5,3),(5,3)]],"Q":1/mpf(3)}
BS25 = {
"g":[mpf(1)/mpf(10),mpf(1)/mpf(10),mpf(1)/mpf(8), mpf(1)/mpf(8)],
"c":[1,1,1,1],"Q":1/mpf(5)}
HH25 = {
"g":[mpf(1)/mpf(5),mpf(1)/mpf(5),mpf(2)/mpf(5), mpf(2)/mpf(5)],
"c":[1,1,1,1],"Q":1/mpf(5)}
aRR3 = {
"g":[mpf(1)/mpf(10), mpf(1)/mpf(10), mpf(3)/mpf(10), mpf(3)/mpf(10)],
"c":[1,1,-1,-1],"Q":mpf(1)/mpf(5)}
particleset = [HH25,aRR3, BS25, LaughlinE5]
names =[ r"$\mathrm{HH}_{2/5}$ (e/5)",
r"$\overline{\mathrm{RR}}_{k=3} $ (e/5)",
r"$\mathrm{BS}_{2/5}$ (e/5)",
r"Laughlin (2e/5)"]
mp.mp.dps= 60
fig = plt.figure()
ax = fig.add_subplot(111)
ans = []
for i in range(len(names)):
particle = genData.copy()
particle.update(particleset[i])
Qe = particle["Q"]
del particle["Q"]
A = base_parameters(particle, V = Vpoints, Q = Qe, T = 1/mpf(10**3))
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 1000, maxA = 12, maxK = 12)
B.genAnswer()
ans.append(B)
ax.plot(Vpoints, B.rrfunction, label = names[i], linewidth=1.5)
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
dashstyle = [(None, None), [10,4], [6,3,1,3,1,3],[2,2] ,[2,6]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
ax.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax.xaxis.set_label_coords(.9, -0.06)
ax.set_ybound([-.5, 1])
ax.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.set_title(r"Modulating function for $\nu = 12/5 $ candidates", fontsize=16)
ax.legend(loc='upper right', prop={'size':14})
ax.grid(True)
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
if saving: plt.savefig('particles_12_5.pdf', bbox_inches=0, dpi=300)
plt.show()
return ans
def particles_5_2(saving = False):
Vpoints = mp.linspace(0, mpf('1.')/mpf(10**4), 201)
dist1 = mpf('2.4')/ mpf(10**(6))
dist2 = mpf('2.1')/mpf(10**(6))
genData = {
"v":[mpf(i) * mpf(10**j) for (i,j) in [(5,3),(5,3),(1.4,3),(1.4,3)]],
"x":[-dist1, dist2, -dist1, dist2]}
pfaffE2 = {
"g":[mpf(1)/mpf(2),mpf(1)/mpf(2)],
"c":[1,1],
"x":[-dist1, dist2],
"v":[mpf(i) * mpf(10**j) for (i,j) in [(5,3),(5,3)]],"Q":1/mpf(2)}
pfaff = {
"g":[mpf(1)/mpf(8), mpf(1)/mpf(8),mpf(1)/mpf(8), mpf(1)/mpf(8)],
"c":[1,1,1,1],"Q":1/mpf(4)}
apf = {
"g":[mpf(1)/mpf(8),mpf(1)/mpf(8),mpf(3)/mpf(8), mpf(3)/mpf(8)],
"c":[1,1,-1,-1],"Q":1/mpf(4)}
state331 = {
"g":[mpf(1)/mpf(8), mpf(1)/mpf(8), mpf(1)/mpf(4), mpf(1)/mpf(4)],
"c":[1,1,1,1],"Q":1/mpf(4)}
particleset = [apf, state331, pfaff, pfaffE2]
names = [
"Anti-Pfaffian (e/4)",
"(3,3,1)-state (e/4)",
"Pfaffian (e/4)",
"Laughlin (e/2)"]
mp.mp.dps= 60
fig = plt.figure()
ax = fig.add_subplot(111)
ans = []
for i in range(0,4):
particle = genData.copy()
particle.update(particleset[i])
Qe = particle["Q"]
del particle["Q"]
A = base_parameters(particle, V = Vpoints, Q = Qe, T = 1/mpf(10**3))
B = Rfunc_constructor(A, method = 'series')
B.setParameter(nterms = 1200, maxA = 12, maxK = 12)
B.genAnswer()
### uncomment to return all instances
# ans.extend([copy.deepcopy(A),copy.deepcopy(B)])
###
if B.rrfunction.shape[1] > 1:
ax.plot(Vpoints, B.rrfunction[:,0], label = names[i], linewidth=1.5)
else:
ax.plot(Vpoints, B.rrfunction, label = names[i], linewidth=1.5)
dashstyle = [(None, None), [10,4], [5,3,1,3], [2,4]]
for i in range(len(ax.get_lines())):
ax.get_lines()[i].set_color('black')
ax.get_lines()[i].set_dashes(dashstyle[i])
ax.set_ylabel(r"$\mathrm{Re}[H_{ij}^{\mathrm{mod}}]{}$", fontsize=16)
ax.set_xlabel(r'Voltage [$\mu$V]', fontsize=16)
ax.xaxis.set_label_coords(.9, -0.06)
ax.set_ybound([-.5, 1])
ax.set_yticks([-0.25, 0, .25, .5, .75, 1])
ax.set_yticklabels([-0.25, 0, 0.25, 0.5, 0.75, 1])
xt = np.linspace(0, 1 * 10**(-4), 5)
xt_labels = [str(int(i * 10**6)) for i in xt]
ax.set_xticks(xt)
ax.set_xticklabels(xt_labels)
ax.set_title(r"Modulating function for $\nu = 5/2 $ candidates", fontsize=16)
ax.legend(loc='upper right', prop={'size':14})
ax.grid(True)
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
if saving: plt.savefig('particles_5_2.pdf', bbox_inches=0, dpi=300)
plt.show()
return ans