Define QN on a sublattice

Question

Hi Miles,

I'm working on a model with conserved quantum number on a sublattice. To be specific, say we have the following Hamiltonian:
$$
H = S{i}^z S{i+1}^z + S_{2i+1}^x
$$
So the total Sz is conserved only for even sites. Is it possible to define a QN for this kind of case? Thanks a lot!

Best,
Chengshu

Answer 1

Hi Chengshu,
Interesting question. My guess is that it should be possible. The main thing that the IQTensor system requires is that some QN be conserved, but I think (or hope) that it should be flexible enough to accomodate a case like this.

Here's how I would approach it: make a new type of SiteSet, similar to SpinHalf (see itensor/mps/sites for examples; definitely use the very latest version of the master branch for this, post 2.0.11 because I've simplified the SiteSet system recently). For the even sites, define the IQIndex's in the same way as the SpinHalf class. For the odd sites, define the IQIndex for each odd site as follows:

IQIndex(nameint("site ",j), Index("0",2,Site), QN("Sz=",0))

In the above, I've merged the usual two IQIndex blocks for a S=1/2 spin (up and down) into a single block of size 2 (indicated by the single Index of size 2) and given this block a QN of Sz=0.

Hopefully this will work, but you may run into an issue somewhere. Please give it a try and let me know if something seems off with your results.

Miles

Comments

That's unfortunate. Can you please compile and re-run the code in debug mode? That way you may get a more helpful error message. Probably I will need to look at the code eventually, because this bug could be related to a deficiency currently in part of the IQTensor system (it's not a bug per se, but just a case that it doesn't handle well).

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In the debug mode even the DMRG is not working, which is really surprising to me. The output now reads

Using approx/svd conversion of AutoMPO->IQMPO
nindex() = 1
i = 1
From line 191, file iqindex.cc

IQIndex::index arg out of range

IQIndex::index arg out of range
Aborted (core dumped)

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So to make things simpler I tried the following "minimum" Hamiltonian
    
    ampo += -4.,"Sp",1,"Sm",2;
    ampo += -4.,"Sm",1,"Sp",2;

And it doesn't work with the following site-setting head file

    s = IQIndex{nameint("S=1/2 ",n),
               Index(nameint("Up ",n),1,Site),QN({1,2}),
               Index(nameint("Dn ",n),1,Site),QN({-1,2})};

I think the problem might be in this parity-conserving QN definition. What do you think about it? Thanks!

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Problem solved! I should have defined the QN as {1,2} and {0,2}. Sorry about the mess!

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Ok great! I meant to write back sooner but this is very good news, as I was initially worried there might be a bug in our IQTensor system. Let me know if you run into any more issues.