def coarse_graining_step_2d(a, b=None, D='infinity'):
A = ncon([a, a], [[-2, -3, -4, 1], [-1, 1, -5, -6]])
U, s, V = tensorsvd(A, [0, 1], [2, 3, 4, 5], D)
A = ncon([U, A, U], [[1, 2, -1], [1, 2, -2, 3, 4, -4], [4, 3, -3]])
if b != None:
B = ncon([b, a], [[-2, -3, -4, 1], [-1, 1, -5, -6]])
B = ncon([U, B, U], [[1, 2, -1], [1, 2, -2, 3, 4, -4], [4, 3, -3]])
AA = ncon([A, A], [[-1, -2, 1, -6], [1, -3, -4, -5]])
U, s, V = tensorsvd(AA, [1, 2], [0, 3, 4, 5], D)
AA = ncon([U, AA, U], [[1, 2, -2], [-1, 1, 2, -3, 4, 3], [3, 4, -4]])
if b != None:
BA = ncon([B, A], [[-1, -2, 1, -6], [1, -3, -4, -5]])
BA = ncon([U, BA, U], [[1, 2, -2], [-1, 1, 2, -3, 4, 3], [3, 4, -4]])
maxAA = np.max(AA)
AA = AA / maxAA #divides over largest value in the tensor
if b != None:
BA = BA / maxAA
else:
BA = AA
return AA, BA, maxAA
def final_contraction(dim, a, b=None):
if dim == 2:
ap = ncon([a, a, a, a],
[[7, 5, 3, 1], [3, 6, 7, 2], [8, 1, 4, 5], [4, 2, 8, 6]])
if b != None:
bp = ncon([b, a, a, a],
[[7, 5, 3, 1], [3, 6, 7, 2], [8, 1, 4, 5], [4, 2, 8, 6]])
elif dim == 3:
ap = ncon([a, a, a, a, a, a, a, a],
[[1, 2, 4, 5, 6, 3], [4, 7, 1, 8, 9, 10],
[11, 12, 13, 14, 3, 6], [13, 15, 11, 16, 10, 9],
[20, 14, 19, 12, 17, 18], [19, 16, 20, 15, 22, 21],
[24, 5, 23, 2, 18, 17], [23, 8, 24, 7, 21, 22]])
if b != None:
bp = ncon([b, a, a, a, a, a, a, a],
[[1, 2, 4, 5, 6, 3], [4, 7, 1, 8, 9, 10],
[11, 12, 13, 14, 3, 6], [13, 15, 11, 16, 10, 9],
[20, 14, 19, 12, 17, 18], [19, 16, 20, 15, 22, 21],
[24, 5, 23, 2, 18, 17], [23, 8, 24, 7, 21, 22]])
if b == None:
bp = None
return ap, bp
def isings2d(beta, h):
H_local = np.array([[-1. - h / 2, 1.], [1., -1. + h / 2]])
Q = np.exp(-beta * H_local)
g = np.zeros((2, 2, 2, 2))
g[0, 0, 0, 0] = 1.
g[1, 1, 1, 1] = -1.
Qsr = scl.sqrtm(Q)
b = ncon([g, Qsr, Qsr, Qsr, Qsr],
[[1, 2, 3, 4], [-1, 1], [-2, 2], [3, -3], [4, -4]])
return b
def isingtpf2d(beta, h):
H_local = np.array([[-1. - h / 2, 1.], [
1., -1. + h / 2
]]) #h is intended to be a small magnetic field to break symmetry
Q = np.exp(-beta * H_local)
delta = np.zeros((2, 2, 2, 2))
delta[0, 0, 0, 0] = 1.
delta[1, 1, 1, 1] = 1.
Qsr = scl.sqrtm(Q)
a = ncon([delta, Qsr, Qsr, Qsr, Qsr],
[[1, 2, 3, 4], [-1, 1], [-2, 2], [3, -3], [4, -4]])
return a
def coarse_graining_step_3d(a, b=None, D='infinity'):
#z direction
A = ncon([a, a], [[-1, -3, -5, -7, 1, -10], [-2, -4, -6, -8, -9, 1]])
Ux, s, V = tensorsvd(A, [2, 3], [0, 1, 4, 5, 6, 7, 8, 9], D)
Uy, s, V = tensorsvd(A, [0, 1], [2, 3, 4, 5, 6, 7, 8, 9], D)
A = ncon([Ux, Uy, A, Uy, Ux],
[[3, 4, -2], [1, 2, -1], [1, 2, 3, 4, 5, 6, 7, 8, -5, -6],
[5, 6, -3], [7, 8, -4]])
if b != None:
B = ncon([b, a], [[-1, -3, -5, -7, 1, -10], [-2, -4, -6, -8, -9, 1]])
B = ncon([Ux, Uy, B, Uy, Ux],
[[3, 4, -2], [1, 2, -1], [1, 2, 3, 4, 5, 6, 7, 8, -5, -6],
[5, 6, -3], [7, 8, -4]])
#y direction
AA = ncon([A, A], [[-1, -2, 1, -6, -7, -8], [1, -3, -4, -5, -9, -10]])
Uz, s, V = tensorsvd(AA, [6, 8], [0, 1, 2, 3, 4, 5, 7, 9], D)
Ux, s, V = tensorsvd(AA, [1, 2], [0, 3, 4, 5, 6, 7, 8, 9], D)
AA = ncon([Uz, Ux, AA, Ux, Uz],
[[5, 7, -5], [1, 2, -2], [-1, 1, 2, -3, 3, 4, 5, 6, 7, 8],
[4, 3, -4], [6, 8, -6]])
if b != None:
BA = ncon([B, A], [[-1, -2, 1, -6, -7, -8], [1, -3, -4, -5, -9, -10]])
BA = ncon([Uz, Ux, BA, Ux, Uz],
[[5, 7, -5], [1, 2, -2], [-1, 1, 2, -3, 3, 4, 5, 6, 7, 8],
[4, 3, -4], [6, 8, -6]])
#x direction
AAAA = ncon([AA, AA], [[-2, -3, -4, 1, -7, -8], [-1, 1, -5, -6, -9, -10]])
Uz, s, V = tensorsvd(AAAA, [6, 8], [0, 1, 2, 3, 4, 5, 7, 9], D)
Uy, s, V = tensorsvd(AAAA, [3, 4], [0, 1, 2, 5, 6, 7, 8, 9], D)
AAAA = ncon([Uz, Uy, AAAA, Uy, Uz],
[[5, 7, -5], [3, 4, -3], [1, 2, -2, 3, 4, -4, 5, 6, 7, 8],
[2, 1, -1], [6, 8, -6]])
if b != None:
BAAA = ncon([BA, AA],
[[-2, -3, -4, 1, -7, -8], [-1, 1, -5, -6, -9, -10]])
BAAA = ncon([Uz, Uy, BAAA, Uy, Uz],
[[5, 7, -5], [3, 4, -3], [1, 2, -2, 3, 4, -4, 5, 6, 7, 8],
[2, 1, -1], [6, 8, -6]])
maxAAAA = np.max(AAAA)
AAAA = AAAA / maxAAAA #divides over largest value in the tensor
if b != None:
BAAA = BAAA / maxAAAA
else:
BAAA = AAAA
return AAAA, BAAA, maxAAAA