AutoMPO to IQMPO Error with user-defined siteset / four-body interactions

Question

Hello,

I want to define a new siteset with two "colors" (A and B) of spin 1/2. We can assume that in a chain lattice odd sites=A and that even sites=B. In my system, @@S^z_\mathrm{tot}@@ of A and B spin is conserved separately. This also means that @@S^z_\mathrm{tot}(A+B)=S^z_\mathrm{tot}(A)+S^z_\mathrm{tot}(B)@@ is conserved.

Using the standard "SpinHalf" siteset would only lead to @@S^z_\mathrm{tot}(A+B)@@ conservation. So I've implemented a new one with two QNs where the only difference with the standard one is

SpinHalfABSite(int n, Args const& args = Args::global())
    {
    if(n%2 == 1)
        s = IQIndex{nameint("S=1/2 (A) ",n),
               Index(nameint("Up ",n),1,Site),QN(+1, 0),
               Index(nameint("Dn ",n),1,Site),QN(-1, 0)};
    else
        s = IQIndex{nameint("S=1/2 (B) ",n),
               Index(nameint("Up ",n),1,Site),QN(0, +1),
               Index(nameint("Dn ",n),1,Site),QN(0, -1)};
    }

I think that at this point, it is correct. The problem is when I want to build an IQMPO through the AutoMPO builder for my specific Hamiltonian,

auto ampo = AutoMPO(sites);
for(int i = 1; i < sites.N(); i += 2)
    {
    for(int j = 1; j < sites.N(); j += 2)
       {
       if(i < j)
            {
            ampo += 1.0,"S+",i,"S-",i+1,"S-",j,"S+",j+1;
            ampo += 1.0,"S-",i,"S+",i+1,"S+",j,"S-",j+1;
            }
        }
    }
auto ham = IQMPO(ampo);

where @@S^\alpha_{i,j}@@ acts on the A spins and @@S^\alpha_{i+1,j+1}@@ on the B ones. However, this leads to the following error,

I = IQIndex(Hl4,2,Link,901) <Out>
  (hl4_0,2,Link,628) QN()
qn = QN(-4,4)
From line 514, file iqindex.cc
IQIndex does not contain given QN block.
IQIndex does not contain given QN block.
Abort trap: 6

I do not get this error when working with only one color of spin (and the same Hamiltonian). The error happens inside the 'compressMPO' function, when making the compressed MPO for the fourth site (no matter the system size, it always happens at the fourth one).

I'm trying to figure out a bit more this part of the ITensor code but if you have any idea of what could be wrong!

Answer 1

Hi, thanks for reporting this. I think what's going on here is actually two separate bugs, one within ITensor and one in your code.

1. The bug within ITensor, now fixed, is that for efficiency AutoMPO was assuming that operators with the same name also carried the same quantum numbers. But that is not the case for your site set and wouldn't be the case e.g. for a site set with different spin types, like a lattice with both spin half and spin one sites. So now AutoMPO doesn't assume that anymore. Please pull the latest version of ITensor from GitHub and recompile and you'll have this fixed version.

2. I believe there's a bug within your code too: you have terms containing things like "S+",i,"S-",i+1 but would not that process fail to conserve A and B total Sz separately? I think maybe you meant for the site to be i and i+2 instead of i and i+1. I could be wrong about this second bug, though, because I didn't do a careful study of it so please just think about it and see if you agree or disagree.

Please let me know if the new version still doesn't work for you. Thanks for pointing out this serious issue!

Miles

Comments

Hi Miles,

Thanks for your answer and the fix! About point 2, I think that the current code is correct, because the Hamiltonian has four-body terms (S+/S- on i/j (odd) sites of color A and S+/S- on i+1/j+1 (even) sites of color B).

Maxime