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Correlation measurement

Technical
2019-08-05
2019-08-08
  • Rafael Barfknecht

    Hello,

    I am trying to compare some correlation results obtained with OSMPS. When creating the operators (for fermions) I define

    myObservables.AddObservable('corr', ['fdagger', 'f'], name='spdm', Phase=True)

    As described in the documentation, this calculates ['fdagger', 'f'] for sites i<=j. The outcome, however, is a LxL matrix (which cannot be filled by only considering i<=j). So how are the extra terms calculated?

    Thanks in advance,

    Rafael B.

     
  • Daniel Jaschke

    Daniel Jaschke - 2019-08-07

    Hi Rafael,

    all two site correlation measurement are defined via two operators L and R. In your example L=fdagger and R=f. Some have an addition phase term including the one you use implicitly defined via Phase=True.

    The diagonal entries are based on a new operator (L * R) via a matrix multiplication. In this specific example, you get the number operator on each site for "free" with the correlation measurement.

    The other entries are the measurement L_i R_j as a two site correlator (i different from j). Now you can have i < j and j < i which explains why both triangles in the correlation matrix are filled.

    For speed, there should actually be a test and if L = R, then we just fill the entries of the second triangular matrix without calculating them in an extra step.

    I hope that gives you a good overview and let us know if you need more details than that.

    Best regards,

    Daniel

     
  • Rafael Barfknecht

    Hi Daniel,

    Thanks for the reply. Right, so I understand that you fill the remaining slots by considering i<j AND j<i. But in the result we see that the out of diagonal elements differ by a minus sign, which indicates that the operators f_dagger and f have been swapped. Is it correct to assume that?

    Best,

    Rafael

     

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