def getChern(omega,
delta,
epsilon,
U,
n,
S,
m0,
kList=np.linspace(-1.0, 1.0, 600),
plot=True):
i = 0
s = int(2 * S + 1)
N = 2 * n + 1
E = np.zeros((kList.size, s * N))
m = np.zeros((kList.size, s * N))
pops = np.zeros((kList.size, s * N, s))
ktot = np.zeros((kList.size, s * N))
mFvect = np.array([np.float(j - S) for j in range(s)])
for k in kList:
H, kstates = RamanLatHam(k, omega, delta, epsilon, U, n, S, m0)
Energies, eigenstates = LA.eig(H)
sort = np.argsort(Energies)
Esorted, eVsorted = Energies[sort], eigenstates[:, sort]
E[i] = Esorted
ev = eVsorted.transpose()
evA = ev.reshape(N * s, N, s)
popsA = np.sum(evA * np.conjugate(evA), axis=1)
pops[i] = popsA
evB = ev.reshape(N * s, N * s)
popsB = evB * np.conjugate(evB)
ktot[i] = np.einsum('i,ji->j', kstates, popsB)
m[i] = np.dot(popsA, mFvect)
i = i + 1
if plot:
cDict = {}
cDict[-2] = 'm-'
cDict[-1] = 'r-'
cDict[0] = 'g-'
cDict[1] = 'b-'
cDict[2] = 'c-'
#
fig5 = plt.figure()
pan5 = fig5.add_subplot(1, 1, 1)
for mF in np.arange(-S, S + 1):
if S <= 2:
pan5.plot(kList,
pops[:, 0, mF + S],
cDict[mF],
label=r'$m_F$=' + str(mF))
else:
pan5.plot(kList,
pops[:, 0,
mF + S]) #, cDict[mF], label=r'$m_F$='+str(mF))
pan5.set_xlabel(r'Crystal momentum [$k_L$]')
pan5.set_ylabel('Fractional populations')
pan5.set_title('Lowest band')
plt.legend()
if c > 0:
indM = kList.size / 6
ind0 = kList.size / 2
indP = 5 * kList.size / 6
elif c < 0:
indM = 5 * kList.size / 6
ind0 = kList.size / 2
indP = kList.size / 6
else:
indM = kList.size / 2
ind0 = kList.size / 2
indP = kList.size / 2
xMth, dxMth = getMaxFitTheory(
kList,
pops[:, 0, S - 1],
np.ones(pops[:, 0].size) * 0.001,
indC=indM,
plot=plot) #[np.where(pops[:,0,S-1]==np.max(pops[:,0,S-1]))]
x0th, dx0th = getMaxFitTheory(kList,
pops[:, 0, S],
np.ones(pops[:, 0].size) * 0.001,
indC=ind0,
plot=plot)
xPth, dxPth = getMaxFitTheory(kList,
pops[:, 0, S + 1],
np.ones(pops[:, 0].size) * 0.001,
indC=indP,
plot=plot)
Ath, Bth, dAth, dBth = lineFit2.lineFit(np.array([xMth, x0th, xPth]),
np.array([-1, 0, 1]),
'q',
'max. m',
errorbars=True,
yerr=np.array(
[dxMth, dx0th, dxPth]),
plot=plot)
print xMth, x0th, xPth
print 'chern theory = ' + str(Ath * 2 / 3) + '+/-' + str(dAth * 2 / 3)
chern = Ath * 2.0 / 3.0
return pops, chern
def getChernTB(omega,
delta,
epsilon,
tx,
S,
m0,
c=4.0 / 3.0,
kList=np.linspace(-1.0, 1.0, 600),
Flat=True,
save=False,
plots=True):
kList, E, m, pops = tbh.plotSynDimBandStructGenTBClean(omega,
delta,
epsilon,
tx,
S,
m0,
c=c,
kList=kList,
Flat=Flat,
save=save,
plots=plots)
if c > 0:
indM = kList.size / 6
ind0 = kList.size / 2
indP = 5 * kList.size / 6
elif c < 0:
indM = 5 * kList.size / 6
ind0 = kList.size / 2
indP = kList.size / 6
else:
indM = kList.size / 2
ind0 = kList.size / 2
indP = kList.size / 2
if plots:
fig = plt.figure()
pan = fig.add_subplot(111)
pan.plot(kList, pops[:, 0, S - 1], 'r-')
pan.plot(kList, pops[:, 0, S], 'g-')
pan.plot(kList, pops[:, 0, S + 1], 'b-')
xMth, dxMth = getMaxFitTheory(
kList,
pops[:, 0, S + 1],
np.ones(pops[:, 0].size) * 0.001,
indC=indM,
plot=plots) #[np.where(pops[:,0,S-1]==np.max(pops[:,0,S-1]))]
x0th, dx0th = getMaxFitTheory(kList,
pops[:, 0, S],
np.ones(pops[:, 0].size) * 0.001,
indC=ind0,
plot=plots)
xPth, dxPth = getMaxFitTheory(kList,
pops[:, 0, S - 1],
np.ones(pops[:, 0].size) * 0.001,
indC=indP,
plot=plots)
Ath, Bth, dAth, dBth = lineFit2.lineFit(np.array([xMth, x0th, xPth]),
np.array([-1, 0, 1]),
'q',
'max. m',
errorbars=True,
yerr=np.array(
[dxMth, dx0th, dxPth]),
plot=plots)
print xMth, x0th, xPth
print 'chern theory = ' + str(Ath * 2 / 3) + '+/-' + str(dAth * 2 / 3)
chern = Ath * 2.0 / 3.0
delChern = dAth * 2.0 / 3.0
# popAvg=np.zeros(pops[:,0,:].shape)
# s=2*S+1
# for ind,k in enumerate(kList):
# for i in range(s):
# popAvg[ind,i]=np.average(pops[ind,0:int(np.ceil(s/q)),i])
#
# xMth,dxMth=getMaxFitTheory(kList,popAvg[:,S+1],np.ones(pops[:,0].size)*0.001,indC=indM,plot=plots) #[np.where(pops[:,0,S-1]==np.max(pops[:,0,S-1]))]
# x0th,dx0th=getMaxFitTheory(kList,popAvg[:,S],np.ones(pops[:,0].size)*0.001,indC=ind0,plot=plots)
# xPth,dxPth=getMaxFitTheory(kList,popAvg[:,S-1],np.ones(pops[:,0].size)*0.001,indC=indP,plot=plots)
#
#
#
# Ath,Bth,dAth,dBth=lineFit2.lineFit(np.array([xMth,x0th,xPth]),np.array([-1,0,1]),'q','max. m',errorbars=True,yerr=np.array([dxMth,dx0th,dxPth]),plot=plots)
# print xMth, x0th, xPth
# print 'chern theory = '+ str(Ath*2/3) + '+/-'+str(dAth*2/3)
#
# chern = Ath*2.0/3.0
# delChern = dAth*2.0/3.0
return pops, chern, delChern
# qlistF2p[i] = qlistF2p[i] + 2.0
#
#A,B,dA,dB = lineFit2.lineFit(tlistF2p,qlistF2p,'','')
#
#qlistF2pFit = tlistF2p*A
#sortF2p=np.argsort(qlistF2pFit)
odF2m = datafileF2m['odFiltAll']
xCentersF2m = datafileF2m['xCenters']
tlistF2m = datafileF2m['tlist']
qlistF2m = datafileF2m['qlist']
for i, q in enumerate(qlistF2m):
if q > -0.8:
qlistF2m[i] = qlistF2m[i] - 2.0
A, B, dA, dB = lineFit2.lineFit(tlistF2m, qlistF2m, '', '')
qlistF2mFit = tlistF2m * A
sortF2m = np.argsort(qlistF2mFit)
figure = plt.figure()
figure.clear()
figure.set_size_inches(3.0, 1.7)
gs = gridspec.GridSpec(5, 1)
gs.update(left=0.05, right=0.95, top=1.0, bottom=0.2, wspace=0, hspace=0)
vmax = 0.4
vmin = 0.0
x0, dx0 = figureChenOfOmegaSize.getMaxFitTheory(qlist,
fraction0,
sigma0,
indC=ind0d,
plot=plotBool)
xM, dxM = figureChenOfOmegaSize.getMaxFitTheory(qlist,
fractionM,
sigmaM,
indC=indMd,
plot=plotBool)
print 'S = ' + str(S)
A, B, dA, dB = lineFit2.lineFit(np.array([xM, x0, xP]),
np.array([-1, 0, 1]),
'q',
'max. m',
errorbars=True,
yerr=np.array([dxM, dx0, dxP]),
plot=plotBool)
print 'chern = ' + str(A * 2 / 3) + '+/-' + str(dA * 2 / 3)
Ath, Bth, dAth, dBth = lineFit2.lineFit(np.array([xMth, x0th, xPth]),
np.array([-1, 0, 1]),
'q',
'max. m',
errorbars=True,
yerr=np.array(
[dxMth, dx0th, dxPth]),
plot=plotBool)
print 'chern theory = ' + str(Ath * 2 / 3) + '+/-' + str(dAth * 2 / 3)
def getChern(omega,
delta,
epsilon,
U,
n,
S,
m0,
kList=np.linspace(-1.0, 1.0, 600),
plot=True):
i = 0
s = int(2 * S + 1)
N = 2 * n + 1
E = np.zeros((kList.size, s * N))
m = np.zeros((kList.size, s * N))
pops = np.zeros((kList.size, s * N, s))
ktot = np.zeros((kList.size, s * N))
mFvect = np.array([np.float(j - S) for j in range(s)])
for k in kList:
H, kstates = RamanLatHam(k, omega, delta, epsilon, U, n, S, m0)
Energies, eigenstates = LA.eig(H)
sort = np.argsort(Energies)
Esorted, eVsorted = Energies[sort], eigenstates[:, sort]
E[i] = Esorted
ev = eVsorted.transpose()
evA = ev.reshape(N * s, N, s)
popsA = np.sum(evA * np.conjugate(evA), axis=1)
pops[i] = popsA
evB = ev.reshape(N * s, N * s)
popsB = evB * np.conjugate(evB)
ktot[i] = np.einsum('i,ji->j', kstates, popsB)
m[i] = np.dot(popsA, mFvect)
i = i + 1
if plot:
cDict = {}
cDict[-2] = 'm-'
cDict[-1] = 'r-'
cDict[0] = 'g-'
cDict[1] = 'b-'
cDict[2] = 'c-'
#
fig5 = plt.figure()
pan5 = fig5.add_subplot(1, 1, 1)
for mF in np.arange(-S, S + 1):
if S <= 2:
pan5.plot(kList,
pops[:, 0, mF + S],
cDict[mF],
label=r'$m_F$=' + str(mF))
else:
pan5.plot(kList,
pops[:, 0,
mF + S]) #, cDict[mF], label=r'$m_F$='+str(mF))
pan5.set_xlabel(r'Crystal momentum [$k_L$]')
pan5.set_ylabel('Fractional populations')
pan5.set_title('Lowest band')
plt.legend()
if c > 0:
indM = kList.size / 6
ind0 = kList.size / 2
indP = 5 * kList.size / 6
elif c < 0:
indM = 5 * kList.size / 6
ind0 = kList.size / 2
indP = kList.size / 6
else:
indM = kList.size / 2
ind0 = kList.size / 2
indP = kList.size / 2
xMth, dxMth = getMaxFitTheory(
kList,
pops[:, 0, S - 1],
np.ones(pops[:, 0].size) * 0.001,
indC=indM,
plot=plot) #[np.where(pops[:,0,S-1]==np.max(pops[:,0,S-1]))]
x0th, dx0th = getMaxFitTheory(kList,
pops[:, 0, S],
np.ones(pops[:, 0].size) * 0.001,
indC=ind0,
plot=plot)
xPth, dxPth = getMaxFitTheory(kList,
pops[:, 0, S + 1],
np.ones(pops[:, 0].size) * 0.001,
indC=indP,
plot=plot)
Ath, Bth, dAth, dBth = lineFit2.lineFit(np.array([xMth, x0th, xPth]),
np.array([-1, 0, 1]),
'q',
'max. m',
errorbars=True,
yerr=np.array(
[dxMth, dx0th, dxPth]),
plot=plot)
print xMth, x0th, xPth
print 'chern theory = ' + str(Ath * 2 / 3) + '+/-' + str(dAth * 2 / 3)
chern = Ath * 2.0 / 3.0
return pops, chern
#q=3.0
#c=4.0/q#1064.0/790.0#0.0#
#Flat=False
#
#omegaList=np.linspace(0.0,2.0,50)
#chernList1=np.zeros(omegaList.size)
#chernList2=np.zeros(omegaList.size)
#for ind, omega in enumerate(omegaList):
# pops, chernList1[ind]=getChern(omega, 0.0, 0.02, 4.4, 7,1,0,kList=np.linspace(-1.0,1.0,200), plot=False)
# pops, chernList2[ind]=getChern(omega, 0.0, 0.02, 4.4, 7,2,0,kList=np.linspace(-1.0,1.0,200), plot=False)
#
#figure=plt.figure()
#pan=figure.add_subplot(111)
#pan.plot(omegaList,chernList1, 'bo')
#pan.set_xlabel(r'$\Omega$ [$E_L$]')
#pan.set_ylabel(r'Chern number')
#
#figure2=plt.figure()
#pan2=figure2.add_subplot(111)
#pan2.plot(omegaList,chernList2, 'bo')
#pan2.set_xlabel(r'$\Omega$ [$E_L$]')
#pan2.set_ylabel(r'Chern number')
#filename = 'ChernOfOmegaNotFlat'
#np.savez(filename, c=c,Flat=Flat, omegaList = omegaList, chernList1=chernList1,chernList2=chernList2,
# delta=0.0,epsilon=0.02,U=4.4,m0=0,kList=np.linspace(-1.0,1.0,200))
#q=3.0
#c=4.0/q#1064.0/790.0#0.0#
#Flat=True
#Slist=np.arange(1,21)
#chernList=np.zeros(Slist.size)
#for ind, Sloc in enumerate(Slist):
# pops, chernList[ind]=getChern(0.5, 0.0, 0.0, 4.4, 7,Sloc,0,kList=np.linspace(-1.0,1.0,200), plot=False)
# print Sloc
#
#
#figure3=plt.figure()
#pan3=figure3.add_subplot(111)
#pan3.plot(Slist,chernList, 'bo')
#pan3.set_xlabel(r'F')
#pan3.set_ylabel(r'Chern number')
#
#filename = 'ChernOfSystemSizeOmega05'
#np.savez(filename, c=c,Flat=Flat, Slist = Slist, chernList=chernList, omega=0.5,delta=0.0,epsilon=0.0,U=4.4,m0=0,kList=np.linspace(-1.0,1.0,200))
pan=fig.add_subplot(gs[i*2])
pan.errorbar(qlist[fitGoodList]/2.0, mode[fitGoodList],yerr=sigmaMode[fitGoodList],fmt='o',color='Grey',markersize=2)
pan.plot(kList[fitGoodTheoryList]/2.0,modeTheory[fitGoodTheoryList],'r-',linewidth=1)
qrangeList = np.linspace(0.2,1.0,20)
Alist = np.zeros(qrangeList.size)
dAlist = np.zeros(qrangeList.size)
numPointsList = np.zeros(qrangeList.size)
for ind,qrange in enumerate(qrangeList):
qrangeBool=((qlist[fitGoodList]<qrange) & (qlist[fitGoodList]>-qrange))
Alist[ind],B,dAlist[ind],dB = lineFit2.lineFit(qlist[fitGoodList][qrangeBool], mode[fitGoodList][qrangeBool],'q data','m data',yerr=sigmaMode[fitGoodList][qrangeBool],plot=False,errorbars=True, bounds=(np.array([-np.inf,-0.001]),np.array([np.inf,0.001])))
numPointsList[ind] = qlist[fitGoodList][qrangeBool].size
#pan.set_xlabel(r'$q_x$ [$k_L$]',size=14)
#pan.set_ylabel(r'$\langle m \rangle$',size=14)
qrangeListTh = np.linspace(0.01,1.0,25)
AlistTh = np.zeros(qrangeListTh.size)
dAlistTh = np.zeros(qrangeListTh.size)
numPointsListTh = np.zeros(qrangeListTh.size)
for ind,qrange in enumerate(qrangeListTh):
krangeBool=((kList[fitGoodTheoryList]<qrange) & (kList[fitGoodTheoryList]>-qrange))
AlistTh[ind],B,dAlistTh[ind],dB = lineFit2.lineFit(kList[fitGoodTheoryList][krangeBool],modeTheory[fitGoodTheoryList][krangeBool],'q theory','m theory',plot=False, bounds=(np.array([-np.inf,-0.001]),np.array([np.inf,0.001])))
numPointsListTh[ind] = kList[fitGoodTheoryList][krangeBool].size
#if clist2[i]!=0:
# axins = inset_axes(pan,
# width="20%", # width = 30% of parent_bbox
# height="30%", # height : 1 inch
TDSEfile['latticeRampOnt'] - TDSEfile['ramanRampOnt']) / (
TDSEfile['tgrid'][-1] * hbar / Erecoil -
TDSEfile['latticeRampOnt'] - TDSEfile['ramanRampOnt'])
modeTDSE = TDSEfile['modeList'][qlistTDSE > 0]
fracs = TDSEfile['fracs'][qlistTDSE > 0]
qlistTDSE = qlistTDSE[qlistTDSE > 0]
qlistTDSE = np.append(-qlistTDSE[::-1], qlistTDSE)
modeTDSE = np.append(-modeTDSE[::-1], modeTDSE)
fracs = np.append(fracs[::-1, ::-1], fracs, axis=0)
pan.plot(qlistTDSE / 2.0, modeTDSE, label=np.round(forcelist[ind], 3))
A, B, dA, dB = lineFit2.lineFit(qlistTDSE,
modeTDSE,
'q theory',
'm theory',
plot=plotBool,
bounds=(np.array([-np.inf, -0.001]),
np.array([np.inf, 0.001])))
chernLine[ind] = A * 2.0 / 3.0
delChernLine[ind] = dA * 2.0 / 3.0
indM = qlistTDSE.size / 6
ind0 = qlistTDSE.size / 2
indP = 5 * qlistTDSE.size / 6
xPth, dxPth = figureChenOfOmegaSize.getMaxFitTheory(
qlistTDSE,
fracs[:, 1],
np.ones(fracs[:, 1].size) * 0.001,
indC=indP,