def test_nonint(self):
#get the exact solution.
h_exact=self.model_exact.hgen.H()
E_excit=eigvalsh(h_exact)
Emin_exact=sum(E_excit[E_excit<0])
#the solution in occupation representation.
h_occ=self.model_occ.hgen.H()
Emin=eigsh(h_occ,which='SA',k=1)[0]
print 'The Ground State Energy for hexagon(t = %s, t2 = %s) is %s, tolerence %s.'%(self.t,self.t2,Emin,Emin-Emin_exact)
assert_almost_equal(Emin_exact,Emin)
#the solution through updates
H_serial=op2collection(op=self.model_occ.hgen.get_opH())
H=get_H(H=H_serial,hgen=self.expander)
H2,bm2=get_H_bm(H=H_serial,hgen=self.expander2,bstr='QM')
Emin=eigsh(H,k=1,which='SA')[0]
Emin2=eigsh(H2,k=1,which='SA')[0]
print 'The Ground State Energy is %s, tolerence %s.'%(Emin,Emin-Emin2)
assert_almost_equal(Emin_exact,Emin)
assert_almost_equal(Emin_exact,Emin2)
#the solution through dmrg.
bmgen=get_bmgen(self.expander3.spaceconfig,'QM')
dmrgegn=DMRGEngine(hchain=H_serial,hgen=self.expander3,tol=0,bmg=bmgen,symmetric=True)
EG2=dmrgegn.run_finite(endpoint=(5,'<-',0),maxN=[10,20,30,40,40],tol=0)[-1]
assert_almost_equal(Emin_exact,EG2*H_serial.nsite,decimal=4)
def get_solving_system(K1,K2,U,nsite,mu=0.,t=1.,evolutor_type='null',periodic=False,perturb=None):
'''
Set the parameters and get the solving system.
Parameters:
:K1,K2,U,mu,t: float, the parameters.
:evolutor_type: str,
* 'null', do not perform any unitary and truncation during expansion of sites.
* 'full', do blockize and unitary but no truncation is allowed.
* 'masked', use kpmask to identify truncation.
Return:
tuple of (model, expander)
'''
assert(evolutor_type in ['null','full','masked'])
model=BizardModel(K1=K1,K2=K2,U=U,t=t,mu=mu,nsite=nsite,periodic=periodic)
if perturb is not None:
if 'bSDW' in perturb.keys():
model.perturb_bSDW(sites=perturb['bSDW'])
elif 'mu' in perturb.keys():
model.perturb_mu(sites=perturb['mu'][0],lamb=perturb['mu'][1])
if evolutor_type=='null':
return model,None
else:
spaceconfig=SuperSpaceConfig(chorder([model.hgen.spaceconfig.nspin,1,model.hgen.spaceconfig.norbit]))
H_serial=op2collection(op=model.hgen.get_opH())
expander=RGHGen(spaceconfig=spaceconfig,H=H_serial,evolutor_type=evolutor_type)
#ion()
#H_serial.show_advanced()
#pdb.set_trace()
return model,expander
def get_opc(self):
'''
Construct <OpCollection> for a chain.
Return:
<OpCollection>, the operator collection.
'''
impurity=self.impurity
bath=self.bath
nsite=bath.nsite+1
spaceconfig1=impurity.spaceconfig
config=list(spaceconfig1.config)
config[-2]=nsite
spaceconfig=SuperSpaceConfig(config)
elist,tlist=self.elist_rescaled,self.tlist_rescaled
tlist2=swapaxes(tlist.conj(),-1,-2)
ebonds=[Bond(zeros(2),i,i) for i in xrange(len(elist))]
tbonds=[Bond([1.,0],i,i+1) for i in xrange(len(tlist))]
tbonds2=[Bond([-1.,0],i+1,i) for i in xrange(len(tlist))]
opc=op_on_bond('E',spaceconfig=spaceconfig,mats=elist,bonds=ebonds)
opc=opc+op_on_bond('T',spaceconfig=spaceconfig,mats=concatenate([tlist2,tlist],axis=0),bonds=tbonds2+tbonds)
opc.label='H'
opc+=impurity.get_interaction()
return op2collection(opc).compactify()
def test_site_image(self):
H_serial = op2collection(op=self.model_occ.hgen.get_opH())
H_serial.insert_Zs(spaceconfig=self.spaceconfig1)
H2 = site_image(H_serial,
care_sign=False,
NL=0,
NR=self.model_exact.nsite)
print H_serial
print H2
def test_disc_symm(self,nsite=40):
'''
The parameters are adapted from PRB 54. 7598
'''
self.set_params(U=4.,t=1.,mu=0.,t2=0.,nsite=nsite)
H_serial=op2collection(op=self.model_occ.hgen.get_opH())
bmgen=get_bmgen(self.expander3.spaceconfig,'QM')
dmrgegn=DMRGEngine(hchain=H_serial,hgen=self.expander3,tol=0,bmg=bmgen,symmetric=True,disc_symm='C')
EG2=dmrgegn.run_finite(endpoint=(4,'->',nsite-2),maxN=[10,20,30,40,40],tol=0,block_params={'target_block':(0,0),'target_sector':{'C':-1}})[-1]
print EG2*nsite
pdb.set_trace()
def test_nonint(self):
#get the exact solution.
spaceconfig = self.spaceconfig1
self.set_params(U=0., t=1., mu=0.2, t2=0., nsite=6)
h_exact = self.model_exact.hgen.H()
E_excit = eigvalsh(h_exact)
Emin_exact = sum(E_excit[E_excit < 0])
#the solution in occupation representation.
h_occ = self.model_occ.hgen.H()
Emin, Vmin1 = eigsh(h_occ, which='SA', k=1)
print 'The Ground State Energy for hexagon(t = %s, t2 = %s) is %s, tolerence %s.' % (
self.t, self.t2, Emin, Emin - Emin_exact)
assert_almost_equal(Emin_exact, Emin)
#the solution through updates
H_serial = op2collection(op=self.model_occ.hgen.get_opH())
H_serial_Z = copy.copy(H_serial)
H_serial_Z.insert_Zs(spaceconfig=spaceconfig)
expander = ExpandGenerator(spaceconfig=spaceconfig,
H=H_serial_Z,
evolutor_type='null',
use_zstring=True)
H = get_H(hgen=expander)
expander2 = ExpandGenerator(spaceconfig=spaceconfig,
H=H_serial_Z,
evolutor_type='normal',
use_zstring=True)
H2, bm2 = get_H_bm(hgen=expander2, bstr='QM')
Emin = eigsh(H, k=1, which='SA')[0]
Emin2 = eigsh(H2, k=1, which='SA')[0]
print 'The Ground State Energy is %s, tolerence %s.' % (Emin,
Emin - Emin2)
assert_almost_equal(Emin_exact, Emin)
assert_almost_equal(Emin_exact, Emin2)
#the solution through dmrg.
expander3 = ExpandGenerator(spaceconfig=spaceconfig,
H=H_serial,
evolutor_type='masked',
use_zstring=True)
dmrgegn = DMRGEngine(hgen=expander3, tol=0, reflect=False)
dmrgegn.use_U1_symmetry('QM', target_block=(0, 0))
EG2, Vmin2 = dmrgegn.run_finite(endpoint=(5, '<-', 0),
maxN=[10, 30, 60, 100, 100],
tol=0)
Vmin2 = fix_tail(Vmin2, expander3.spaceconfig, 0)
#check for states.
assert_almost_equal(Emin_exact, EG2, decimal=4)
Vmin1 = Vmin1[:, 0]
assert_almost_equal(abs(Vmin2.state), abs(Vmin1), decimal=3)
print(Vmin2.state / Vmin1)[abs(Vmin1) > 1e-2]
pdb.set_trace()
def test_disc_symm(self, nsite=40):
'''
The parameters are adapted from PRB 54. 7598
'''
self.set_params(U=2., t=1., mu=1., t2=0., nsite=nsite)
spaceconfig = self.spaceconfig1
H_serial = op2collection(op=self.model_occ.hgen.get_opH())
expander3 = ExpandGenerator(spaceconfig=spaceconfig,
H=H_serial,
evolutor_type='masked',
use_zstring=True)
dmrgegn = DMRGEngine(hgen=expander3, tol=0, reflect=True)
dmrgegn.use_U1_symmetry('QM', target_block=(0, 0))
for c in [-1, 1]:
dmrgegn.use_disc_symmetry(target_sector={'C': c}, detect_scope=4)
EG2, EV2 = dmrgegn.run_finite(endpoint=(5, '<-', 0),
maxN=[20, 40, 100, 100, 100],
tol=0)
print 'Get gound state energy for C2 -> %s: %s.' % (c, EG2)
#the result is -36.1372 for C=-1, and -36.3414 for C=1
pdb.set_trace()
def solve_update(model,expander,k=10,target_block=None,**kwargs):
'''
Solve using chain updates.
'''
H_serial=op2collection(op=model.hgen.get_opH())
#ion()
#H_serial.show_advanced()
#pdb.set_trace()
t0=time.time()
if isinstance(expander.evolutor,NullEvolutor):
H=get_H(H=H_serial,hgen=expander)
Emin,Evec=eigsh(H,k=k,which='SA',maxiter=5000,v0=random.random(H.shape[0]))
else:
H2,bm2=get_H_bm(H=H_serial,hgen=expander,bstr=model.qnumber)
if target_block is not None:
if hasattr(target_block,'__call__'):
target_block=target_block(model.nsite)
H2=bm2.lextract_block(H2,target_block)
Emin,Evec=eigsh(H2,k=k,which='SA',v0=random.random(H2.shape[0]))
t1=time.time()
print 'The Ground State Energy for %s: %s, Elapse %s.'%(model,array(sorted(Emin)),t1-t0)
return Emin,Evec
def get_solving_system(alpha,Vz,Delta,U,nsite,mu=0.,t=1.,evolutor_type='null',periodic=True):
'''
Set the parameters and get the solving system.
Parameters:
:alpha,Vz,Delta,U,mu,t: float, the parameters.
:evolutor_type: str,
* 'null', do not perform any unitary and truncation during expansion of sites.
* 'full', do blockize and unitary but no truncation is allowed.
* 'masked', use kpmask to identify truncation.
Return:
tuple of (model, expander)
'''
assert(evolutor_type in ['null','full','masked'])
model=RashbaModel(alpha=alpha,Vz=Vz,U=U,Delta=Delta,t=t,mu=mu,nsite=nsite,periodic=periodic,occ=True,kspace=False)
spaceconfig=model.hgen.spaceconfig
spaceconfig1=SuperSpaceConfig(chorder([1,spaceconfig.nspin,1,spaceconfig.norbit]))
H_serial=op2collection(op=model.hgen.get_opH())
expander=RGHGen(H=H_serial,spaceconfig=spaceconfig1,evolutor_type=evolutor_type,use_zstring=True)
return model,expander
def solve_update(model,expander,k=1):
'''
Solve using chain updates.
'''
H_serial=op2collection(op=model.hgen.get_opH())
ion()
#H_serial.show_advanced()
t0=time.time()
if isinstance(expander.evolutor,NullEvolutor):
H=get_H(H=H_serial,hgen=expander)
Emin,Evec=eigsh(H,k=k,which='SA',tol=1e-12)
else:
H2,bm2=get_H_bm(H=H_serial,hgen=expander,bstr='P')
print bm2.check_blockdiag(H2)
H_even=bm2.lextract_block(H2,0)
H_odd=bm2.lextract_block(H2,1)
Emin_even,Evec_even=eigsh(H_even,k=k,which='SA',tol=1e-12)
Emin_odd,Evec_odd=eigsh(H_odd,k=k,which='SA',tol=1e-12)
#Emin,Evec=eigsh(H2,k=k,which='SA',tol=1e-12)
t1=time.time()
print 'The Ground State Energy for model %s is %s(even),%s(odd): diff -> %s, Elapse -> %s.'%(
model,Emin_even.min(),Emin_odd.min(),Emin_odd.min()-Emin_even.min(),t1-t0)
return Emin_even,Evec_even,Emin_odd,Evec_odd
def solve1(delta,target_block,nsite,override=True,C2parity=None,t=1.,mu=0.):
'''Get and store the eigen vectors and eigen values for ground state.'''
model=SSHModel(delta=delta,t=t,mu=mu,nsite=nsite,manybody=True)
suffix='%s_%s.dat'%(model.get_str(),target_block)
filename_mps='data/mps3_'+suffix
filename_eng='data/eng3_'+suffix
if not override and os.path.isfile(filename_mps):
Ei=loadtxt(filename_eng)[0]
return Ei,MPS.load(filename_mps)
spaceconfig=SuperSpaceConfig(chorder([model.hgen.spaceconfig.nspin,1,model.hgen.spaceconfig.norbit]))
H_serial=op2collection(op=model.hgen.get_opH())
expander=RGHGen(spaceconfig=spaceconfig,H=H_serial,evolutor_type='masked')
t0=time.time()
dmrgegn=DMRGEngine(hgen=expander,tol=1e-7,reflect=False,eigen_solver='JD') #we can not use reflect here, because SOC do not meet reflection condition!
dmrgegn.use_U1_symmetry('PM',target_block=target_block)
Emin,mps=dmrgegn.run_finite(endpoint=(5,'<-',0),maxN=[10,25,50,70,70,70,70],tol=1e-8)
t1=time.time()
print 'The Ground State Energy for %s: %s, Elapse %s.'%(model,Emin,t1-t0)
print 'FIN - CORE:%s'%RANK
mps.save(filename_mps)
savetxt(filename_eng,Emin)
return Emin,mps
def solve_dmrg(model,expander,target_block,maxsweep=None,maxN=None,nlevel=1,C2parity=None,**kwargs):
'''
Solve using DMRG.
'''
nsite=model.nsite
if nsite<=60:mN=100
if nsite<=80:mN=150
else: mN=200 #not accurate any more!
if maxN is None:
maxN=[25,40,80,80,80] if not ONSV else [25,60,80,100,mN,mN,mN,mN]
if maxsweep is None:
maxsweep=4 if not ONSV else 7
t0=time.time()
H_serial=op2collection(op=model.hgen.get_opH())
dmrgegn=DMRGEngine(hgen=expander,tol=1e-10,reflect=C2parity is not None,eigen_solver='JD')
dmrgegn.use_U1_symmetry(model.qnumber,target_block=target_block)
if C2parity is not None:
dmrgegn.use_disc_symmetry(target_sector={'C':C2parity},detect_scope=2)
Emin,Vmin=dmrgegn.run_finite(endpoint=(maxsweep,'<-',0),maxN=maxN,\
tol=1e-7,nlevel=nlevel,call_before=kwargs.get('call_before'),call_after=kwargs.get('call_after'))
Emin=Emin[0]
t1=time.time()
print 'The Ground State Energy for %s, C2 -> %s: %s, Elapse %s.'%(model,C2parity,Emin,t1-t0)
return Emin,Vmin
