def cal_dos_mf(Vz,Delta,mu=0.,**kwargs):
'''
show the meanfield band.
'''
model=RashbaModel(Vz=Vz,Delta=Delta,mu=mu,**kwargs)
filename_dos='data/dos_%s.dat'%model.get_str()
filename_mj='data/mf_%s.npy'%model.get_str()
hgen=model.hgen
if kwargs.get('kspace'):
kl=hgen.kspace.kmesh
hmesh=hgen.gethkmesh(kl)
else:
hmesh=hgen.H(dense=True)
#tridmat=sr2trid(hmesh)
#g=tinv(tridmat)
hmesh=Hmesh(hmesh)
emesh,vmesh=hmesh.getemesh(evalvk=True)
wlist=linspace(-3,3,501)
wlist,dos=Emesh(emesh).show_dos(wlist,geta=3e-3)
dosdata=concatenate([wlist[:,newaxis],dos[:,newaxis]],axis=1)
savetxt(filename_dos,dosdata)
if not kwargs.get('kspace'):
gate=0.01
has_mf=Vz>Delta and abs(mu)<sqrt(Vz**2-Delta**2)
print 'Has Majorana fermion: %s.'%has_mf
mjmask=abs(emesh)<gate
print 'Zero Energy States(abs(E) < %s) -> %s'%(gate,emesh[mjmask])
mjdata=vmesh[:,mjmask]
save(filename_mj,mjdata)
def plot_dos(delta=0.1,t=1.,mu=0.,kspace=False,nsite=100,**kwargs):
'''
show the meanfield band.
'''
model=SSHModel(t=t,delta=delta,nsite=nsite,mu=mu,kspace=kspace,**kwargs)
hgen=model.hgen
if kspace:
kl=hgen.kspace.kmesh
hmesh=hgen.gethkmesh(kl)
else:
hmesh=hgen.H()
hmesh=Hmesh(hmesh)
emesh,vmesh=hmesh.getemesh(evalvk=True)
wlist=linspace(-3,3,200)
gate=0.01
frmask=abs(emesh)<gate
vs=vmesh[:,frmask]
print 'Zero Energy States(abs(E) < %s) -> %s'%(gate,emesh[frmask])
ion()
subplot(121)
Emesh(emesh).show_dos(wlist,geta=3e-3)
subplot(122)
plot(vs)
xlim(-1,nsite*2)
pdb.set_trace()
def plot_band(alpha,Vz,Delta,t=1.,mu=0.,nsite=100):
'''
show the meanfield band.
'''
model=RashbaModel(U=0.,alpha=alpha,Vz=Vz,Delta=Delta,t=t,mu=mu,nsite=nsite,periodic=True,kspace=True)
hgen=model.hgen
kl=hgen.kspace.kmesh-pi
hkmesh=hgen.gethkmesh(kl)
hmesh=Hmesh(hkmesh)
print hmesh.check_hermicity()
ekmesh=hmesh.getemesh()
LABELSIZE=14
ion()
fig=figure(figsize=(7,5))
plot(kl[:,0],ekmesh)
if True:#hgen.spaceconfig.nnambu==1:
axhline(y=0,ls='--',color='k')
text(1.8,-0.1,'$\mu=0$',ha='center',va='center',fontsize=14)
if Vz==0 and alpha!=0:
dy=alpha**2/2
annotate('',xy=(-alpha,-2*dy),xycoords='data',xytext=(alpha,-2*dy),\
arrowprops=dict(arrowstyle='<->',shrinkA=0,shrinkB=0))
plot([-alpha,-alpha],[-dy-0.1,-dy+0.1],color='k',ls='-')
plot([alpha,alpha],[-dy-0.1,-dy+0.1],color='k',ls='-')
text(0,-2*dy-0.1,r'$2\alpha$',va='center',ha='center',fontsize=14)
xlabel(r'$k$',fontsize=LABELSIZE)
ylabel('Energy($t$)')
xlim(-pi,pi)
xticks([-pi,0,pi],[r'$-\pi/a$','0',r'$-\pi/a$'],fontsize=14)
tight_layout()
pdb.set_trace()
savefig('data/band_%s.png'%model.get_str())
def test_exp_k(self):
t=random.random()
Tlist=[0,0.5]
Hk=lambda k:2*t*cos(k)*identity(2)
klist=arange(1000)*2*pi/1000
hmesh=Hmesh([Hk(k) for k in klist])
E,U=hmesh.getemesh(evalvk=True)
for T in Tlist:
mval=rFij(E=E,U=U,T=T)
assert_allclose(mval[0].diagonal(),0.5*ones(mval.shape[1]))
def plot_band_mf(M,t=1.):
'''
show the meanfield band.
'''
model=BizardModel_MF(M=M,t=t,mu=0.,N=100,periodic=True,usekspace=True)
hgen=model.hgen
kl=kmesh=linspace(0,pi,400)
hkmesh=hgen.gethkmesh(kl[:,newaxis])
hmesh=Hmesh(hkmesh)
ekmesh=hmesh.getemesh()
ion()
plot(kl,ekmesh)
pdb.set_trace()
def plot_band(delta=0.1,t=1.,mu=0.,nsite=100):
'''
show the meanfield band.
'''
model=SSHModel(t=t,mu=mu,delta=delta,nsite=nsite,periodic=True,kspace=True)
hgen=model.hgen
kl=hgen.kspace.kmesh-pi
hkmesh=hgen.gethkmesh(kl)
hmesh=Hmesh(hkmesh)
print hmesh.check_hermicity()
ekmesh=hmesh.getemesh()
ion()
plot(kl[:,0],ekmesh)
pdb.set_trace()
def perco_fuliang():
'''
Get the bulk entanglement spectrum for Fu Liang's work.
'''
model,perco=get_models(L=5,size=5,form='x',N=100)
hgen=model.hgen
kspace=perco.get_kspace()
kpath=path_k([kspace.G,kspace.special_points['X'][0],kspace.M[0],kspace.G],N=50)
ion()
cfunc=lambda k:EU2C(*eigh(hgen.Hk(k)),T=0.1)
ck_red=perco.reduce_k(cfunc,kpath)
hkmesh=Hmesh(C2H(ck_red,T=1.))
ekmesh=hkmesh.getemesh()
kpath.plot(ekmesh,mode='abs')
ylim(-5,5)
pdb.set_trace()
def measure_charge_MF(M,t=1.,nsite=6):
'''
show the meanfield band.
'''
model=BizardModel_MF(M=M,t=t,mu=0.02,N=nsite,periodic=False,usekspace=False)
hgen=model.hgen
hmesh=hgen.H()
hmesh=Hmesh(hmesh)
emesh,vmesh=hmesh.getemesh(evalvk=True)
cmesh=EU2C(emesh,vmesh)
dos=[]
for i in xrange(nsite):
mask=hgen.spaceconfig.atomindexer==i
dos.append(sum(cmesh[mask,mask]))
ion()
plot(dos)
ylim(0,2)
pdb.set_trace()
def test_symm(self,useC=True):
perco=self.get_perco(L=5,size=5,form='x')
hgen=self.model.hgen
kspace=perco.get_kspace()
kpath=path_k([kspace.G,kspace.special_points['X'][0],kspace.M[0],kspace.G],N=40)
ion()
if useC:
cfunc=lambda k:EU2C(*eigh(hgen.Hk(k)),T=0.1)
ck_red=perco.reduce_k(cfunc,kpath)
hkmesh=Hmesh(C2H(ck_red,T=1.))
else:
hfunc=lambda k:hgen.Hk(k)
hk_red=perco.reduce_k(hfunc,kpath)
hkmesh=Hmesh(hk_red)
ekmesh=hkmesh.getemesh()
kpath.plot(ekmesh,mode='abs',ls='--' if useC else '-')
ylim(-5,5)
pdb.set_trace()
def plot_dos(M,t=1.,periodic=True,usekspace=True,N=100):
'''
show the meanfield band.
'''
model=BizardModel_MF(M=M,t=t,mu=0.,N=N,periodic=periodic,usekspace=usekspace)
hgen=model.hgen
if usekspace:
kl=hgen.kspace.kmesh
hmesh=hgen.gethkmesh(kl[:,newaxis])
else:
hmesh=hgen.H()
hmesh=Hmesh(hmesh)
emesh=hmesh.getemesh()
ion()
wlist=linspace(-3,3,200)
Emesh(emesh).show_dos(wlist)
gate=0.01
print 'Zero Energy States(abs(E) < %s) -> %s'%(gate,emesh[abs(emesh)<gate])
pdb.set_trace()
def test_bandrecover(self,useC=True):
perco=self.get_perco(L=1,size=1,form='#')
T=1.
hgen=self.model.hgen
kspace=perco.get_kspace()
kpath=path_k([kspace.G,kspace.special_points['X'][0],kspace.M[0],kspace.G],N=50)
if useC:
cfunc=lambda k:EU2C(*eigh(hgen.Hk(k)),T=T)
ck_red=perco.reduce_k(cfunc,kpath)
hkmesh=Hmesh(C2H(ck_red))
else:
hfunc=lambda k:hgen.Hk(k)
hk_red=perco.reduce_k(hfunc,kpath)
hkmesh=Hmesh(hk_red)
ekmesh=hkmesh.getemesh()
ekmesh0=Hmesh([hgen.Hk(k) for k in kpath]).getemesh()
#kpath.plot(ekmesh,mode='abs')
#kpath.plot(ekmesh0,mode='abs',color='r',ls='--')
assert_allclose(ekmesh,ekmesh0,atol=1e-4)
