Measuring the double occupancy of an MPS wavefunction

Question

Hello,
Working with the Hubbard class, I'm trying to compute the double occupancy
$$
d=\sum{i=1}^{L} \langle n{i \uparrow} n_{i \downarrow} \rangle .
$$
Browsing through the documentation, I found two possible syntaxes for defining the corresponding operator at site i, namely:

ITensor dop1 = sites.op("Nupdn",i);
ITensor dop2 = sites.op("Nup*Ndn",i);

and both give the correct result.
However, after reading the documentation page about local measurements (http://itensor.org/docs.cgi?page=formulas/measure_mps) it is very tempting to try to define the double occupancy operator as:

ITensor dop3 = sites.op("Nup",i)*sites.op("Ndn",i); 

This syntax, however, raises a "Mismatched IQIndex arrows" error.
Any thoughts about this?

Answer 1

Hi, that's good about the first approaches giving you what you needed to measure.

About the last line of code, if you draw the tensor diagrams (do Print(sites.op(...,i)); to see a printout of the indices), paying close attention to the arrows and prime levels you'll see what the * operation is trying to do, and why it fails. The rule about arrows is that contracted IQIndices must have opposite arrow directions.

To correctly multiply two operator-like tensors, you can use the multSiteOps function. It's actually just a little 3 line function you would probably have no trouble implementing yourself (basically just raise the prime level of the second op by 1 then to mapprime(result, 2,1) at the end).

Miles

Comments

Got it. Thanks for the answer, Miles.