def test_fct(a, A):
X = peps.make_double_layer(a, o=gates.sigmax)
Z = peps.make_double_layer(a, o=gates.sigmaz)
def test_fct_impl(e):
e1 = e.get_site_environment()
mx = e1.contract(X) / e1.contract(A)
e2 = e.get_bond_environment()
czz = e2.contract(Z, Z) / e2.contract(A, A)
return -2*czz - h*mx
return test_fct_impl
def get_energy(a, returnmz=False):
global env
a = get_symm_tensor(a)
A = peps.make_double_layer(a)
tester = ctm.CTMRGGenericTester(test_fct(a, A), 1e-9)
env = ctm.ctmrg_1x1_hermitian(A, chi, env, tester)
E = tester.get_value()
if returnmz:
e = env.get_site_environment()
Z = peps.make_double_layer(a, o=gates.sigmaz)
mz = e.contract(Z) / e.contract(A)
return E, mz
return E
def test_fct(a, A):
n = len(a)
Z = map(lambda b: peps.make_double_layer(b, o=gates.sigmaz), a)
AT = map(lambda B: B.transpose([1, 2, 3, 0]), A)
ZT = map(lambda B: B.transpose([1, 2, 3, 0]), Z)
X = map(lambda b: peps.make_double_layer(b, o=gates.sigmax), a)
Y = map(lambda b: peps.make_double_layer(b, o=gates.sigmay), a)
XT = map(lambda B: B.transpose([1, 2, 3, 0]), X)
YT = map(lambda B: B.transpose([1, 2, 3, 0]), Y)
def test_fct_impl(e):
c_zz = 0
c_xx = 0
c_yy = 0
mz = [0, 0]
for j in xrange(n):
e1 = e.get_site_environment(j)
mz[j] = e1.contract(Z[j]) / e1.contract(A[j])
e2 = e.get_bond_environment_horizontal(j)
norm = e2.contract(A[j], A[lut[j, 1, 0]])
c_xx += e2.contract(X[j], X[lut[j, 1, 0]]) / norm
c_yy += np.real(e2.contract(Y[j], Y[lut[j, 1, 0]]) / norm)
c_zz += e2.contract(Z[j], Z[lut[j, 1, 0]]) / norm
e2 = e.get_bond_environment_vertical(j)
norm = e2.contract(AT[j], AT[lut[j, 0, 1]])
c_xx += e2.contract(XT[j], XT[lut[j, 0, 1]]) / norm
c_yy += np.real(e2.contract(YT[j], YT[lut[j, 0, 1]]) / norm)
c_zz += e2.contract(ZT[j], ZT[lut[j, 0, 1]]) / norm
c_xx /= 2 * n
c_yy /= 2 * n
c_zz /= 2 * n
E = 2 * J * (c_xx + c_yy + c_zz) + h * 0.5 * (mz[0] + mz[1])
return mz + [c_xx, c_yy, c_zz, E]
return test_fct_impl
def test_fct(a, A):
n = len(a)
X = map(lambda b: peps.make_double_layer(b, o=gates.sigmax), a)
Z = map(lambda b: peps.make_double_layer(b, o=gates.sigmaz), a)
AT = map(lambda B: B.transpose([1,2,3,0]), A)
ZT = map(lambda B: B.transpose([1,2,3,0]), Z)
def test_fct_impl(e):
mx = 0
mz = 0
czz = 0
S = 0 # some pseudo entanglement entropy
for j in xrange(n):
e1 = e.get_site_environment(j)
norm = e1.contract(A[j])
mx += e1.contract(X[j]) / norm
mz += e1.contract(Z[j]) / norm
e2 = e.get_bond_environment_horizontal(j)
norm = e2.contract(A[j], A[lut[j,1,0]])
czz += e2.contract(Z[j], Z[lut[j,1,0]]) / norm
e2 = e.get_bond_environment_vertical(j)
norm = e2.contract(AT[j], AT[lut[j,0,1]])
czz += e2.contract(ZT[j], ZT[lut[j,0,1]]) / norm
w1 = np.dot(e.c1[j], e.c2[lut[j,1,0]])
w2 = np.dot(e.c3[lut[j,1,1]], e.c4[lut[j,0,1]])
xi = np.linalg.svd(np.dot(w1, w2))[1]
xi = xi[np.nonzero(xi)]
S += np.dot(xi**2, np.log(xi))
E = (-czz - h*mx) / n
mz /= n
return [mz, S, E]
return test_fct_impl
def get_energy(a, returnmz=False):
global env
a = get_symm_tensor(a)
A = peps.make_double_layer(a)
f = test_fct(a, A)
tester = ctm.CTMRGGenericTester(f, 1e-12)
#env = ctm.ctmrg([A], lut, chi, env, tester)
#env = ctm.ctmrg_1x1_rotsymm(A, chi, env, tester)
env = ctm.ctmrg_1x1_hermitian(A, chi, env, tester)
#env2 = ctm.CTMEnvironment(lut, env.c, env.c, env.c, env.c, env.t1, env.t2, env.t1, env.t2)
#tester = ctm.CTMRGGenericTester(f, 1e-8)
#env2 = ctm.ctmrg([A], lut, chi, env2, tester)
E = tester.get_value()
if returnmz:
e = env.get_site_environment()
Z = peps.make_double_layer(a, o=gates.sigmaz)
mz = e.contract(Z) / e.contract(A)
return E, mz
return E
def correlation_fct(component):
X = map(lambda b: peps.make_double_layer(b, o=sigma[component]), a)
mx = m[component]
tmp = tdot(env.c4[lut[0,-1,-1]], env.t4[lut[0,-1,0]], [1,0])
tmp = tdot(tmp, env.c1[lut[0,-1,1]], [2,0])
tmp = tdot(tmp, env.t3[lut[0,0,-1]], [0,2])
tmp2 = tdot(tmp, X[0], [[3,0],[2,3]])
uX = tdot(tmp2, env.t1[lut[0,0,1]], [[0,2],[0,1]]).flatten()
tmp2 = tdot(tmp, A[0], [[3,0],[2,3]])
uA = tdot(tmp2, env.t1[lut[0,0,1]], [[0,2],[0,1]]).flatten()
vX = [None]*n
vA = [None]*n
for j in xrange(n):
tmp = tdot(env.c3[lut[j,1,-1]], env.t2[lut[j,1,0]], [0,2])
tmp = tdot(tmp, env.c2[lut[j,1,1]], [1,1])
tmp = tdot(tmp, env.t3[lut[j,0,-1]], [0,0])
tmp2 = tdot(tmp, X[j], [[0,2],[1,2]])
vX[j] = tdot(tmp2, env.t1[lut[j,0,1]], [[0,2],[2,1]]).flatten()
tmp2 = tdot(tmp, A[j], [[0,2],[1,2]])
vA[j] = tdot(tmp2, env.t1[lut[j,0,1]], [[0,2],[2,1]]).flatten()
M = [None]*n
for j in xrange(n):
tmp = tdot(env.t3[lut[j,0,-1]], A[j], [1,2])
tmp = tdot(tmp, env.t1[lut[j,0,1]], [2,1])
M[j] = tmp.transpose([1,3,4,0,2,5]).reshape(len(vX[lut[j,-1,0]]), len(vX[lut[j,1,0]]))
res = np.empty(Lmax+1)
j = lut[0,1,0]
for L in xrange(Lmax+1):
print L
res[L] = np.dot(uX, vX[j]) / np.dot(uA, vA[j]) - mx[0]*mx[j]
if L < Lmax:
uX = np.dot(uX, M[j])
uA = np.dot(uA, M[j])
j = nns[0][j]
return res
outfile = sys.argv[2]
chi = int(sys.argv[3])
Lmax = int(sys.argv[4])
def test_fct(e):
mz = [0]*n
for j in xrange(n):
e1 = e.get_site_environment(j)
mz[j] = e1.contract(Z[j]) / e1.contract(A[j])
return mz
a, nns = peps.load(statefile)
n = len(a)
lut = util.build_lattice_lookup_table(nns, [4,4])
A = map(peps.make_double_layer, a)
Z = map(lambda b: peps.make_double_layer(b, o=gates.sigmaz), a)
tester = ctm.CTMRGTester(test_fct, 1e-12, 1e-15)
env = ctm.ctmrg(A, lut, chi, "random", tester)
m = np.empty((3, n))
sigma = [gates.sigmax, np.imag(gates.sigmay), gates.sigmaz]
# note: handle take sigmay/i instead of sigmay and multiply with (1/i)^2 = -1
for j in xrange(n):
e1 = env.get_site_environment(j)
for k in xrange(3):
op = sigma[k]
O = peps.make_double_layer(a[j], o=op)
m[k,j] = e1.contract(O) / e1.contract(A[j])
