How create a mps like (|up>+|Dn>)_1(|up>-|Dn>)_2|up>+|Dn>)_3(|up>-|Dn>)_4....

ITensor C++ Questions
1

Dear evergone，

I need to generate a state in the form MPS. The state is

(|up>+|dn>)_1 (|up>-|dn>)_2 (|up>+|dn>)_3 (|up>-|dn>)_4....(|up>+|dn>)_{N-1} (|up>-|dn>)_N.

Looking forward to your reply
Thanks

2

The Hadamard gate (or matrix) acting on up or down will do this for you
H|\uparrow\rangle = 1/\sqrt{2} (|\uparrow\rangle +|\downarrow\rangle) \\ H|\downarrow\rangle = 1/\sqrt{2} (|\uparrow\rangle -|\downarrow\rangle)
So start with the antiferromagnetic |\uparrow\downarrow\uparrow\dots\uparrow\downarrow\rangle state as an MPS, then apply the single site itensor/gate to each site. This isn’t built in to the C++ version, so you’ll need to make the op yourself (It’s built in to the Julia version))

You can also just write out the tensors directly if thats easier, this is a MPS with bond dimension of 1

1 Like
3

Thanks.
I solved this problem，for Spin-1 chain

auto psiz4 = MPS(sites);
for(int i=1; i<=N; i++){
if(i%2==1 ){
auto si = sites(i);
auto wf = ITensor(si);
wf.set(si(1), 1./sqrt(2));
wf.set(si(2), 0.0) ;
wf.set(si(3), 1./sqrt(2));
psiz4.setA(i,wf);
}
else
{
auto si = sites(i);
auto wf = ITensor(si);
wf.set(si(1), 1./sqrt(2));
wf.set(si(2), 0.0) ;
wf.set(si(3), -1./sqrt(2));
psiz4.setA(i,wf);}
}

4

Great! Just a small thing, be careful since the MPS you created has no link indices, so certain algorithms may not work as expected (e.g. inner(psiz4,H,psiz4) will error but DMRG seems to work)

5

Good point, Ryan.

Jie, as a workaround in case you have any issues related to the lack of link indices, you can just call:
orthogonalize!(psi,1)
on your MPS psi and that ought to put the link indices in for you.

6

I use function Apply,inner(psiz4,Apply(H,psiz4)). Yours is better.