def testTDVP_SEXPMV(self):
N=self.N
self.dmrg.__simulateTwoSite__(4,1e-10,1e-6,40,verbose=1,solver='LAN')
edmrg=self.dmrg.__simulate__(2,1e-10,1e-10,30,verbose=1,solver='LAN')
self.dmrg._mps.__applyOneSiteGate__(np.asarray([[0.0,1.],[0.0,0.0]]),int(self.N/2))
self.dmrg._mps.__position__(self.N)
self.dmrg._mps.__position__(0)
self.dmrg._mps.resetZ() #don't forget to normalize the state again after application of the gate
engine=en.TimeEvolutionEngine(self.dmrg._mps,self.mpo,"TDVP_insert_name_here")
Dmax=32 #maximum bond dimension to be used during simulation; the maximally allowed bond dimension of the mps will be
#adapted to this value in the TimeEvolutionEngine
thresh=1E-16 #truncation threshold
SZ=np.zeros((self.Nmax,N)) #container for holding the measurements
plt.ion()
sz=[np.diag([-0.5,0.5]) for n in range(N)] #a list of local operators to be measured
it1=0 #counts the total iteration number
it2=0 #counts the total iteration number
tw=0 #accumulates the truncated weight (see below)
solver='SEXPMV'
for n in range(self.Nmax):
#measure the operators
L=engine.measureLocal(sz)
#store result for later use
SZ[n,:]=L
it1=engine.doTDVP(self.dt,numsteps=self.numsteps,krylov_dim=10,cnterset=it1,solver=solver)
print(" : ",np.linalg.norm(SZ-self.Szexact)/(self.Nmax*self.N))
self.assertTrue(np.linalg.norm(SZ-self.Szexact)/(self.Nmax*self.N)<1E-8)
dmrg.simulate(3, 1e-10, 1e-10, 30, verbose=1, solver='LAN')
dmrg._mps.position(0)
#initialize a TimeEvolutionEngine with an mps and an mpo
#you don't have to pass an mpo here; the engine mererly assumes that
#the object passed implements the memberfunction object.twoSiteGate(m,n,dt)
#which should return an twosite gate
dmrg._mps.applyOneSiteGate(np.asarray([[0.0, 1.], [0.0, 0.0]]), 50)
dmrg._mps.position(N)
dmrg._mps.position(0)
#initialize a TEBDEngine with an mps and an mpo
#you don't have to pass an mpo here; the engine mererly assumes that
#the object passed implements the memberfunction object.twoSiteGate(m,n,dt)
#which should return an twosite gate
engine = en.TimeEvolutionEngine(dmrg._mps, mpo, "insert_name_here")
dt = -1j * 0.05 #time step
numsteps = 20 #numnber of steps to be taken in between measurements
Dmax = 40 #maximum bond dimension to be used during simulation; the maximally allowed bond dimension of the mps will be
#adapted to this value in the TEBDEngine
thresh = 1E-8 #truncation threshold
Nmax = 1000 #number of measurements
SZ = np.zeros((Nmax, N)) #container for holding the measurements
plt.ion()
sz = [np.diag([-0.5, 0.5])
for n in range(N)] #a list of local operators to be measured
it = 0 #counts the total iteration number
tw = 0 #accumulates the truncated weight (see below)
for n in range(Nmax):
#measure the operators
def run_sim(dmrgcontainer,solver):
dmrgcontainer._mps.__applyOneSiteGate__(np.asarray([[0.0,1.],[0.0,0.0]]),int(self.N/2))
dmrgcontainer._mps.__position__(self.N)
dmrgcontainer._mps.__position__(0)
engine1=en.TimeEvolutionEngine(dmrgcontainer._mps,self.mpo,"insert_name_here")
engine2=en.TimeEvolutionEngine(dmrgcontainer._mps.__copy__(),self.mpo,"TDVP_insert_name_here")
engine1._mps.resetZ()
engine2._mps.resetZ()
Dmax=32 #maximum bond dimension to be used during simulation; the maximally allowed bond dimension of the mps will be
#adapted to this value in the TimeEvolutionEngine
thresh=1E-16 #truncation threshold
SZ1=np.zeros((self.Nmax,N)).astype(complex) #container for holding the measurements
SZ2=np.zeros((self.Nmax,N)).astype(complex) #container for holding the measurements
SX1=np.zeros((self.Nmax,N)).astype(complex) #container for holding the measurements
SX2=np.zeros((self.Nmax,N)).astype(complex) #container for holding the measurements
SY1=np.zeros((self.Nmax,N)).astype(complex) #container for holding the measurements
SY2=np.zeros((self.Nmax,N)).astype(complex) #container for holding the measurements
plt.ion()
sz=[np.diag([-0.5,0.5]) for n in range(N)] #a list of local operators to be measured
sy=[np.asarray([[0,-0.5j],[0.5j,0]]) for n in range(N)] #a list of local operators to be measured
sx=[np.asarray([[0,1.0],[1.0,0]]) for n in range(N)] #a list of local operators to be measured
it1=0 #counts the total iteration number
it2=0 #counts the total iteration number
tw=0 #accumulates the truncated weight (see below)
for n in range(self.Nmax):
#measure a list of local operators
#L=[engine1._mps.measureLocal(np.diag([-0.5,0.5]),site=n).real for n in range(N)]
SZ1[n,:],SY1[n,:],SX1[n,:]=engine1.measureLocal(sz),engine1.measureLocal(sy),engine1.measureLocal(sx)
#store result for later use
#note: when measuring with measureLocal function, one has to update the simulation container after that.
#this is because measureLocal shifts the center site of the mps around, and that causes inconsistencies
#in the simulation container with the left and right environments
#L=[engine2._mps.measureLocal(np.diag([-0.5,0.5]),site=n).real for n in range(N)]
#engine2.update()
SZ2[n,:],SY2[n,:],SX2[n,:]=engine2.measureLocal(sz),engine2.measureLocal(sy),engine2.measureLocal(sx)
tw,it2=engine1.doTEBD(dt=self.dt,numsteps=self.numsteps,Dmax=Dmax,tr_thresh=thresh,\
cnterset=it2,tw=tw)
it1=engine2.doTDVP(self.dt,numsteps=self.numsteps,krylov_dim=10,cnterset=it1,solver=solver)
plt.figure(1,figsize=(10,8))
plt.clf()
plt.subplot(3,3,1)
plt.plot(range(self.N),self.Szexact[n,:],range(self.N),np.real(SZ2[n,:]),'rd',range(self.N),np.real(SZ1[n,:]),'ko',Markersize=5)
plt.ylim([-0.5,0.5])
plt.xlabel('lattice site n')
plt.ylabel(r'$\langle S^z_n\rangle$')
plt.legend(['exact','TDVP ('+solver+')','TEBD'])
plt.subplot(3,3,4)
plt.semilogy(range(self.N),np.abs(self.Szexact[n,:]-np.real(SZ2[n,:])))
plt.xlabel('lattice site n')
plt.ylabel(r'$|\langle S^z_n\rangle_{tdvp}-\langle S^z_n\rangle_{exact}|$')
plt.subplot(3,3,7)
plt.semilogy(range(self.N),np.abs(self.Szexact[n,:]-np.real(SZ1[n,:])))
plt.xlabel('lattice site n')
plt.ylabel(r'$|\langle S^z_n\rangle_{tebd}-\langle S^z_n\rangle_{exact}|$')
plt.tight_layout()
plt.subplot(3,3,2)
plt.plot(range(self.N),self.Syexact[n,:],range(self.N),np.real(SY2[n,:]),'rd',range(self.N),np.real(SY1[n,:]),'ko',Markersize=5)
plt.ylim([-0.5,0.5])
plt.xlabel('lattice site n')
plt.ylabel(r'$\langle S^y_n\rangle$')
plt.legend(['exact','TDVP ('+solver+')','TEBD'])
plt.subplot(3,3,5)
plt.semilogy(range(self.N),np.abs(self.Syexact[n,:]-np.real(SY2[n,:])))
plt.xlabel('lattice site n')
plt.ylabel(r'$|\langle S^y_n\rangle_{tdvp}-\langle S^y_n\rangle_{exact}|$')
plt.subplot(3,3,8)
plt.semilogy(range(self.N),np.abs(self.Syexact[n,:]-np.real(SY1[n,:])))
plt.xlabel('lattice site n')
plt.ylabel(r'$|\langle S^y_n\rangle_{tebd}-\langle S^y_n\rangle_{exact}|$')
plt.tight_layout()
plt.subplot(3,3,3)
plt.plot(range(self.N),self.Sxexact[n,:],range(self.N),np.real(SX2[n,:]),'rd',range(self.N),np.real(SX1[n,:]),'ko',Markersize=5)
plt.ylim([-0.5,0.5])
plt.xlabel('lattice site n')
plt.ylabel(r'$\langle S^x_n\rangle$')
plt.legend(['exact','TDVP ('+solver+')','TEBD'])
plt.subplot(3,3,6)
plt.semilogy(range(self.N),np.abs(self.Sxexact[n,:]-np.real(SX2[n,:])))
plt.xlabel('lattice site n')
plt.ylabel(r'$|\langle S^x_n\rangle_{tdvp}-\langle S^x_n\rangle_{exact}|$')
plt.subplot(3,3,9)
plt.semilogy(range(self.N),np.abs(self.Sxexact[n,:]-np.real(SX1[n,:])))
plt.xlabel('lattice site n')
plt.ylabel(r'$|\langle S^x_n\rangle_{tebd}-\langle S^x_n\rangle_{exact}|$')
plt.tight_layout()
plt.figure(2)
plt.clf()
plt.subplot(3,1,1)
plt.plot(range(self.N),np.imag(SZ2[n,:]),'rd',range(self.N),np.imag(SZ1[n,:]),'ko',Markersize=5)
plt.xlabel('lattice site n')
plt.ylabel(r'$\Im\langle S^z_n\rangle$')
plt.legend(['TDVP ('+solver+')','TEBD'])
plt.tight_layout()
plt.subplot(3,1,2)
plt.plot(range(self.N),np.imag(SY2[n,:]),'rd',range(self.N),np.imag(SY1[n,:]),'ko',Markersize=5)
plt.xlabel('lattice site n')
plt.ylabel(r'$\Im\langle S^y_n\rangle$')
plt.legend(['TDVP ('+solver+')','TEBD'])
plt.tight_layout()
plt.subplot(3,1,3)
plt.plot(range(self.N),np.imag(SX2[n,:]),'rd',range(self.N),np.imag(SX1[n,:]),'ko',Markersize=5)
plt.xlabel('lattice site n')
plt.ylabel(r'$\Im\langle S^x_n\rangle$')
plt.legend(['TDVP ('+solver+')','TEBD'])
plt.tight_layout()
plt.draw()
plt.show()
plt.pause(0.01)