# Unstable behavior of the self-defined MPO's

**URL:** <https://itensor.discourse.group/t/unstable-behavior-of-the-self-defined-mpos/622>\
**Category:** DMRG and Numerical Methods\
**Created:** [February 2, 2023, 6:05pm UTC](https://itensor.discourse.group/t/unstable-behavior-of-the-self-defined-mpos/622 "2023-02-02T18:05:55Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![tymek](https://avatars.discourse-cdn.com/v4/letter/t/b487fb/32.png) [@tymek](https://itensor.discourse.group/u/tymek)\
**Post date:** [February 2, 2023, 6:05pm UTC](https://itensor.discourse.group/t/unstable-behavior-of-the-self-defined-mpos/622/1 "2023-02-02T18:05:55Z")

</div>

Dear Itensor Community,

I am currently working on structure factors of Bond Order Waves in 1D Hubbard model.  
such a structure factor can be obtained through calculation of the following corelator:

\langle k\_i k\_j \rangle

,where k\_i = \sum\_{\sigma=(\uparrow,\downarrow)}c\_{i+1,\sigma}c\_{i,\sigma} + H.c .

Therefore one obtains a four point correlation function. Therefore, I have defined it in the following way:

```julia
function EHM_Correlators(psi::MPS,N::Int,sites)

sites = siteinds("Electron", N, conserve_qns=true);
replace_siteinds(psi,sites)

BCDW = Array{Float64}(undef,N, N);
BSDW = Array{Float64}(undef,N, N);
for i in 1:N-1
    for j in i+2:N-1

   # sites = siteinds("Electron", N, conserve_qns=true);
   # replace_siteinds(psi,sites)
        
    KCmpo = OpSum()
    KSmpo = OpSum()

    KCmpo += 1.0, "Cdagup", i+1,"Cup", i, "Cdagup", j+1,"Cup", j;
    KCmpo += 1.0, "Cdagup", i+1,"Cup", i, "Cdagdn", j+1,"Cdn", j;
    KCmpo += 1.0, "Cdagup", i+1,"Cup", i, "Cup", j+1,"Cdagup", j;
    KCmpo += 1.0, "Cdagup", i+1,"Cup", i, "Cdn", j+1,"Cdagdn", j;

    KCmpo += 1.0, "Cdagdn", i+1,"Cdn",i, "Cdagup", j+1,"Cup", j;
    KCmpo += 1.0, "Cdagdn", i+1,"Cdn",i , "Cdagdn", j+1,"Cdn", j;
    KCmpo += 1.0, "Cdagdn", i+1,"Cdn",i , "Cup", j+1,"Cdagup", j;
    KCmpo += 1.0, "Cdagdn", i+1,"Cdn",i , "Cdn", j+1,"Cdagdn", j;

    KCmpo += 1.0, "Cup", i+1,"Cdagup", i, "Cdagup", j+1,"Cup", j;
    KCmpo += 1.0, "Cup", i+1,"Cdagup", i, "Cdagdn", j+1,"Cdn", j;
    KCmpo += 1.0, "Cup", i+1,"Cdagup", i, "Cup", j+1,"Cdagup", j;
    KCmpo += 1.0, "Cup", i+1,"Cdagup", i, "Cdn", j+1,"Cdagdn", j;

    KCmpo += 1.0, "Cdn", i+1,"Cdagdn", i, "Cdagup", j+1,"Cup", j;
    KCmpo += 1.0, "Cdn", i+1,"Cdagdn", i, "Cdagdn", j+1,"Cdn", j;
    KCmpo += 1.0, "Cdn", i+1,"Cdagdn", i, "Cup", j+1,"Cdagup", j;
    KCmpo += 1.0, "Cdn", i+1,"Cdagdn", i, "Cdn", j+1,"Cdagdn", j;
    
    KC = MPO(KCmpo, sites);

    BCDW[i,j] = inner(psi',KC,psi)
    BCDW[j,i] = (inner(psi',KC,psi))'
    end
end

end

```

However, many times such matrix gives weird values, like 1e300, and other times it produces reasonable/correct results. I am kind of lost since cannot track the source of the problem further. I tried to replace site indeces inside the loop as well (as I commented in the code), since I thought the generation of MPO in every iteration might cause some problem with that.

I would very thankful for your help or any tips. If needed, I could also provide a minimal working example, but I quite sure the problem does not lie in the wave function.

---

<div class="post-metadata">

**Author:** ![tymek](https://avatars.discourse-cdn.com/v4/letter/t/b487fb/32.png) [@tymek](https://itensor.discourse.group/u/tymek)\
**Post date:** [February 3, 2023, 2:49pm UTC](https://itensor.discourse.group/t/unstable-behavior-of-the-self-defined-mpos/622/2 "2023-02-03T14:49:46Z")

</div>

I think where the error was. Let me confirm on monday.