left - canonize SU2 symmetric tensor

[MaarHybrid]

Hello i want to make tensors left-canonized for SU(2) symmetry and there was some problem. I want to maintain reduced matrix shapes, and want to make norm of mps to be 1.

I tried code below,

from pyblock2._pyscf.ao2mo import integrals as itg
from pyblock2.driver.core import DMRGDriver, SymmetryTypes
from pyblock2.algebra.io import MPSTools
from pyblock2.algebra.core import MPS, SubTensor, Tensor
from pyscf import gto, scf
import numpy as np

bond_dims = [512]
noises = [1e-5]
thrds = [1e-10]

mol = gto.M(atom="N 0 0 0; N 0 0 1.0", basis="sto-3g", symmetry="d2h", verbose=0)
mf = scf.RHF(mol).run(conv_tol=1E-14)
ncas, n_elec, spin, ecore, h1e, g2e, orb_sym = itg.get_rhf_integrals(mf,
    ncore=0, ncas=None, g2e_symm=8)

driver = DMRGDriver(scratch="./tmp", symm_type=SymmetryTypes.SU2, n_threads=4)
driver.initialize_system(n_sites=ncas, n_elec=n_elec, spin=spin, orb_sym=orb_sym)

mpo = driver.get_qc_mpo(h1e=h1e, g2e=g2e, ecore=ecore, iprint=0)
ket = driver.get_random_mps(tag="GS", bond_dim=bond_dims[0], nroots=1)
energy = driver.dmrg(mpo, ket, n_sweeps=100, bond_dims=bond_dims, noises=noises,
    thrds=thrds, iprint=0)

driver.align_mps_center(ket, ref=0)
ket = driver.adjust_mps(ket, dot=1)[0]
pyket = MPSTools.from_block2(ket)

t = pyket.tensors[1]
for b in t.blocks:
    print(b.reduced.shape, b.q_labels)

# GENERATE SAME SHAPED RANDOM MPS
tensor_set = []
for t in pyket:
    tensor = Tensor(blocks=[SubTensor(b.q_labels, 0.2*np.random.randn(*b.reduced.shape)) for b in t.blocks])
    tensor_set.append(tensor)

random_mps = MPS(tensor_set)
random_mps.canonicalize(ncas)

random_ket = MPSTools.to_block2(random_mps, basis=driver.basis, tag="random_MPS")
impo = driver.get_identity_mpo()

print(driver.expectation(random_ket,impo,random_ket))

driver.align_mps_center(random_ket, ref=0)
random_ket = driver.adjust_mps(random_ket, dot=1)[0]
pyrandom_ket = MPSTools.from_block2(random_ket)

t = pyrandom_ket.tensors[1]
for b in t.blocks:
    print(b.reduced.shape, b.q_labels)

And result was below

(3, 1, 10) (< N=2 S=0 PG=0 >, < N=0 S=0 PG=0 >, < N=2 S=0 PG=0 >)
(3, 1, 12) (< N=2 S=0 PG=0 >, < N=1 S=1/2 PG=5 >, < N=3 S=1/2 PG=5 >)
(3, 1, 7) (< N=2 S=0 PG=0 >, < N=2 S=0 PG=0 >, < N=4 S=0 PG=0 >)
(5, 1, 12) (< N=1 S=1/2 PG=0 >, < N=0 S=0 PG=0 >, < N=1 S=1/2 PG=0 >)
(5, 1, 11) (< N=1 S=1/2 PG=0 >, < N=1 S=1/2 PG=5 >, < N=2 S=0 PG=5 >)
(5, 1, 11) (< N=1 S=1/2 PG=0 >, < N=1 S=1/2 PG=5 >, < N=2 S=1 PG=5 >)
(5, 1, 12) (< N=1 S=1/2 PG=0 >, < N=2 S=0 PG=0 >, < N=3 S=1/2 PG=0 >)
(4, 1, 6) (< N=0 S=0 PG=0 >, < N=0 S=0 PG=0 >, < N=0 S=0 PG=0 >)
(4, 1, 12) (< N=0 S=0 PG=0 >, < N=1 S=1/2 PG=5 >, < N=1 S=1/2 PG=5 >)
(4, 1, 10) (< N=0 S=0 PG=0 >, < N=2 S=0 PG=0 >, < N=2 S=0 PG=0 >)

3.000000000000001

(1, 1, 2) (< N=2 S=0 PG=0 >, < N=0 S=0 PG=0 >, < N=2 S=0 PG=0 >)
(1, 1, 1) (< N=2 S=0 PG=0 >, < N=1 S=1/2 PG=5 >, < N=3 S=1/2 PG=5 >)
(1, 1, 1) (< N=2 S=0 PG=0 >, < N=2 S=0 PG=0 >, < N=4 S=0 PG=0 >)
(1, 1, 1) (< N=1 S=1/2 PG=0 >, < N=0 S=0 PG=0 >, < N=1 S=1/2 PG=0 >)
(1, 1, 1) (< N=1 S=1/2 PG=0 >, < N=1 S=1/2 PG=5 >, < N=2 S=0 PG=5 >)
(1, 1, 1) (< N=1 S=1/2 PG=0 >, < N=1 S=1/2 PG=5 >, < N=2 S=1 PG=5 >)
(1, 1, 1) (< N=1 S=1/2 PG=0 >, < N=2 S=0 PG=0 >, < N=3 S=1/2 PG=0 >)
(1, 1, 1) (< N=0 S=0 PG=0 >, < N=0 S=0 PG=0 >, < N=0 S=0 PG=0 >)
(1, 1, 1) (< N=0 S=0 PG=0 >, < N=1 S=1/2 PG=5 >, < N=1 S=1/2 PG=5 >)
(1, 1, 2) (< N=0 S=0 PG=0 >, < N=2 S=0 PG=0 >, < N=2 S=0 PG=0 >)

So there is two problems, first norm of random_ket is not 1, and second reduced matrix's shapes has changed. How can i make tensors for each site left-canonized while maintaining every reduced matrix's shapes?

Thank you

[hczhai]

Tensor with non-abelian symmetry (such as SU2) is complicated, and its manipulation is not supported in pyblock2.algebra.core. For example, MPS.canonicalize is not going to work for non-abelian symmetry. In general, the non-abelian symmetry support in block2 is limited and we do not recommend the user to change the tensor content with SU2 symmetry.

[MaarHybrid]

It's so sad that i have to construct it manually. Thank you for reply