[julia] TEBD gates involving fermions

Question

Dear all,

I am trying to generalize the TEBD method mentioned here to a case involving fermions. When changing the following part

gates = ITensor[]
for j=1:N-1
  s1 = s[j]
  s2 = s[j+1]
  hj =       op("Sz",s1) * op("Sz",s2) +
     1/2 * op("S+",s1) * op("S-",s2) +
     1/2 * op("S-",s1) * op("S+",s2)
  Gj = exp(-1.0im * tau/2 * hj)
  push!(gates,Gj)
end

to include some fermion operators, do we need to manually add JW strings? I am not sure whether these gates already implement JW string like OpSum or not.

Best,
Junsen

Answer 1

Hi Junsen,

Good question. If you switch to using operators like "Cdag" and "C", the evolution should just work. In practice, the fermion sign is handled with fermionic swap gates. If you apply local gates, there are no extra signs needed beyond those that might be within the operators themselves, and if you apply nonlocal gates, our fermionic swap system should handle the signs properly.

Please try it out and let us know if you come across any issues.

Cheers,
Matt

Comments

Hi Matt,

Thank you for the answer. Now I am quite curious about the "fermionic swap gate" you mentioned. How does it handle the fermion sign? Do you have any useful/pedagogical doc or papers on this topic?

Best,
Junsen

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Via a quick googling, I find this answer
https://physics.stackexchange.com/questions/536643/quantum-gate-fswap-acting-on-two-fermion-states
Is it the fermioned swap gate you implied?

---

Yes, that is the most basic version of the kind of swap gate we use.