def getStats(Htot):
def getEnt(EnergyState):#finds entanglement entropy for a given state of H(phi)
Exstate = Ex.Expand(EnergyState,S,N,Jcurr)
RhoA = VN.bipartDM(Exstate,Na,Nb)
eigsA = np.linalg.eigvals(RhoA)
return(np.mean(VN.VNEnt(eigsA)).real)
def getAGR(sortedEn):
Adgphi = []#find all adgr(r) for a given phi, but each phi corresponds to a unique Hamiltonian i.e. H(phi)
for n in range(1,len(sortedEn)-1):
Enb = sortEn[n+1]
Ena = sortEn[n-1]
En = sortEn[n]
AGn = Enb - En
AGa = En - Ena
A = min(AGn,AGa)/max(AGn,AGa)
Adgphi.append(A)
return(Adgphi)
Energy, EnergyStates = fs.filterHstates(Htot,Nstates)#filter states close to energy density
sortEn = sorted(Energy)
Entropies = map(getEnt,EnergyStates)
AGRs = getAGR(sortEn)
return(list(Entropies), list(AGRs))
def getEntropies(Htot):
Energy, EnergyStates = fs.filterHstates(
Htot, Nstates) #filter states close to energy density
#Entropies = []
def getEnt(EnergyState):
Exstate = Ex.Expand(EnergyState, S, N, Jcurr)
RhoA = VN.bipartDM(Exstate, Na, Nb)
eigsA = np.linalg.eigvals(RhoA)
return (VN.VNEnt(eigsA))
return (np.mean(list(map(getEnt, EnergyStates))))
def getAGRs(Htot):
def getAGR(sortedEn):
Adgphi = []#find all adgr(r) for a given phi, but each phi corresponds to a unique Hamiltonian i.e. H(phi)
for n in range(1,len(sortedEn)-1):
Enb = sortEn[n+1]
Ena = sortEn[n-1]
En = sortEn[n]
AGn = Enb - En
AGa = En - Ena
A = min(AGn,AGa)/max(AGn,AGa)
Adgphi.append(A)
return(Adgphi)
Energy= fs.filterEnVals(Htot,Nstates)#filter states close to energy density
sortEn = sorted(Energy)
AGR1 = getAGR(sortEn)
return(list(AGR1))
def getEvecsvals(Htot):
vals, vecs = fs.filterHstates(
Htot, Nstates
) #gets closest Nstates to given energy density (enden). enden is default 0.5
return (vals, vecs)
aV = np.mean([0.25 * term1(envec) - term2(envec)**2 for envec in envecs])
return (aV)
phis = np.linspace(-np.pi * 0.5, np.pi * 0.5, 10)
gammas = np.linspace(0, 8, 50)
Vars = []
for gamma1 in gammas:
Var = []
start = time.time()
for phi1 in phis:
Htot = sum(
H.nlegHeisenberg.blockH(N,
S,
nlegs,
c,
gamma=[0, gamma1],
phi=[0, phi1])).todense()
eneigs, envecs = fs.filterHstates(Htot, Nstates)
Var.append(avgVar(envecs))
Vars.append(np.mean(Var))
end = time.time()
print(end - start)
plt.plot(gammas, Vars)
plt.show()
def DisVEntOld(N,
Nlegs,
Na,
Nb,
phiamt,
Nstates=30,
Jcurr=0,
J1=1,
J2=0,
gamamt=50,
modex2='open',
modey2='open'):
'''
N = 16
Nstates = 30
Jcurr = 0
phiamt = 100
gamamt = 50
Nlegs = 8
Na = 8
Nb = 8
J1=1
J2=1
'''
#print('here')
S = 0.5
c = np.sqrt(2)
phis = np.linspace(-np.pi * 0.5, np.pi * 0.5, phiamt)
gammas = np.linspace(0.5, 8, gamamt)
betas = [c, 0]
NAsites = [0, 1, 2, 3, 4, 5, 6, 7]
NBsites = [8, 9, 10, 11, 12, 13, 14, 15]
SA = []
for gamma1 in gammas:
Ent1 = []
start1 = time.time()
for phi1 in phis:
Hfull = H.nlegHeisenberg.blockH(
N,
S,
Nlegs,
c,
Js=[J1, J2],
gamma=[0, gamma1],
phi=[0, phi1],
modex1=modex2,
modey1=modey2
) #H.TwoDHeisenberg.H(N,Nlegs,S,J = [-1,0],delx=del1,dely=del2,delz=del3,beta=betas,gamma=[gammas[i],0],phi = [phis[j],0])#H.OneDHeisenberg.H(N,S,J1=-1,gamma=gammas[i],beta=c,phi=phis[j], mode='open')### Generate Hamiltonian
Htot = sum(Hfull)
#end1 = time.time()
#print('Hamiltonian Generateion time:', end1-start1)
#H1 = rows@[email protected]#Reduce to Sz=Jcurr Hamiltonian
#start = time.time()
Energy, EnergyStates = fs.filterHstates(
Htot, Nstates) #filter states close to energy density
#Entropies = []
for EnergyState in EnergyStates:
Exstate = Ex.Expand(
EnergyState, S, N, Jcurr
) #expand reduced-hamiltonian state to hilbert space of full hamiltonian
#print(Exstate.tolist())
#RhoA = VN.reducedDM(EnergyState,NAsites,NBsites,N,S,Jcurr=Jcurr)
RhoA = VN.bipartDM(Exstate, Na, Nb)
#print(RhoA)
eigsA = np.linalg.eigvals(RhoA)
Ent1.append(VN.VNEnt(eigsA))
SA.append(np.mean(Ent1).real)
end = time.time()
print('Time for one phi:', end - start1)
#print(np.mean(Ent1))
#SA.append(np.mean(Ent1))
str1 = pl.PurePath(modex2 + 'x_' + modey2 + 'y')
path = pl.PurePath(
os.getcwd()
).parent / 'Data' / str1 / 'Entropy' ###path and filepaths are objects which allow
print(str(path))
filename = '%dx%d_%dphis_%dNstates_J1_%d__J2_%d__%dgammas_Na_%d__Nb_%d__%sx_%sy' % (
N / Nlegs, Nlegs, phiamt, Nstates, J1, J2, gamamt, Na, Nb, modex2,
modey2)
filepath = path / filename
np.save(str(filepath), SA)