def get_Sm():
Sm = PArray([[1], [0, 1], [0, 1]], [[1], [1, 1], [1, 1]])
Sm[0, 1, 0] = np.array(1).reshape(1, 1, 1)
return Sm
def get_Sp():
Sp = PArray([[1], [0, 1], [0, 1]],
[[1], [1, 1], [1, 1]]) # To match with PEPS qnums!
Sp[0, 0, 1] = np.array(1).reshape(1, 1, 1)
return Sp
idx += 1
return x
def fromBits2Conf(bt,nr,nc):
conf = np.zeros([nr,nc], dtype=np.int)
idx = 0
for i in range(nr):
for j in range(nc):
if bits.testBit(bt,idx): conf[i,j] = 1
idx += 1
return conf
#
# Heisenberg Hamiltonian
#
SzMat = np.array([[0.5,0.],[0.,-0.5]])
SpMat = np.array([[0. ,1.],[0.,0. ]])
SmMat = np.array([[0. ,0.],[1.,0. ]])
def genHeisenbergHmn(m,n,mtx):
diff = m^n # xor: 0,1->1; 1,0->1
ndiff = bits.bitCount(diff)
Hmn = 0.
if ndiff == 0:
for i in range(mtx.shape[0]):
for j in mtx.rows[i]:
# (a,b) or (b,a)
if bits.testBit(m,i)^bits.testBit(m,j):
Hmn -= 0.25
# (a,a) or (b,b)
else:
def get_Sz():
Sz = PArray([[0, 1], [0, 1]], [[1, 1], [1, 1]])
Sz[0, 0] = np.array(0.5).reshape(1, 1)
Sz[1, 1] = np.array(-0.5).reshape(1, 1)
return Sz
def test_mc(vec, nr, nc, pdim, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
# Initialization
auxbond = 20
configa = np.zeros([nr, nc], dtype=np.int)
configb = np.zeros([nr, nc], dtype=np.int)
for i in range(nr):
for j in range(nc):
configa[i, j] = (i + j) % 2
configb[i, j] = (i + j + 1) % 2
assert np.sum(configa) % 2 == 0
assert np.sum(configb) % 2 == 0
def genWs(by):
cy = mc_helper.fromBits2Conf(by, nr, nc)
py = peps.create(pdim, cy)
wy = peps.dot(py, P, auxbond)
return wy
mtx = mc_helper.genHeisenbergHlst(nr, nc)
x = mc_helper.fromConf2Bits(configa)
wsx = genWs(x)
nsample = 10000
maxiter = 30
sample = [x] * nsample
ws = np.array([wsx] * nsample)
iop = 1
for niter in range(maxiter):
print '\nniter=', niter
for i in range(nsample):
bx = sample[i]
wx = ws[i]
by = mc_helper.genHeisenbergMove(bx, nr, nc)
wy = genWs(by)
if niter == 0: # accept all
print 'i=', i, bin(by)
sample[i] = by
ws[i] = wy
else:
prob = min([1, (wy / wx)**2])
rand = np.random.rand()
if prob > rand:
sample[i] = by
ws[i] = wy
else:
sample[i] = bx
ws[i] = wx
print 'i=', i, prob, rand, 'accept=', prob > rand
# Compute energy
z = np.sum(ws**2)
eloc = np.zeros(nsample)
# E = 1/Z*sum_S |<P|S>|^2*Eloc
if iop == 0:
# Eloc = <P|H|S>/<P|S> (Variational?)
for i in range(nsample):
by = sample[i]
cy = mc_helper.fromBits2Conf(by, nr, nc)
py = peps.create(pdim, cy)
PHP = peps_h.eval_heish(P, py, auxbond)
eloc[i] = PHP / ws[i]
print 'i=', i, eloc[i]
else:
# Eloc = sum_S' <P|S'><S'|H|S>/<P|S>
# We need a way to generate S' from <S'|H|S>
for i in range(nsample):
sample2 = mc_helper.genHeisenbergConnected(sample[i], nr, nc)
hs = map(
lambda s1: mc_helper.genHeisenbergHmn(s1, sample[i], mtx),
sample2)
wsp = map(lambda s1: genWs(s1), sample2)
eloc[i] = np.dot(wsp, hs) / ws[i]
print 'i=', i, eloc[i]
#
# THIS IS WRONG !!! SIMPLE AVERAGE IS OK.
#
esum = np.dot(eloc, ws**2) / z
print 'etot=', esum, ' e_per_site=', esum / (nr * nc)
return 0