ITensor Developers,
I asked a related question yesterday, but the term I’m trying to create is different, so I created a new topic. Sorry in advance if this was the wrong choice.
How can I add a pinning/next nearest neighbor pairing term to a Hubbard Hamiltonian in Julia? It seems like ITensor doesn’t recognize “hd” or “h” as variables in function main(; Nx = a, Ny=b....) . If its helpful, I’m using ITensors 0.5.2 and ITensorMPS 0.2.1.
The term I’m trying to introduce is given in equation 5 of this paper:
https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.031016
Please excuse me if this is an easy one to answer, I’ve been in Condensed Matter physics for a while but I’m quite new to Julia and ITensor and am not quite sure if I’m looking in the right places for answers to general questions like this.
ITensors is very general, so variables relating to a specific systems would not be predefined in that way. You’ll want to modify your functions to take an h or hd or have the variables defined properly. I recommend hard coding while debugging if that is easier, then rewriting your code to be more general.
I suggest making a Hamiltonian with the OpSum system like the examples. The OpSum function has a sort of “write what you see” approach, so if you have
h c^\dagger_{\uparrow i}c_{\downarrow j}
The OpSum term would be
os = OpSum()
# insert other terms here
# ....
i, j = 1,2 # something
os += h, "Cdagup", i, "Cdn", j
In my other reply was how to add a set of hoppings \sum_\sigma c^\dagger_{\sigma i} c_{\sigma i+1} + h.c., so you can modify this and add appropriate terms to have any number of neighbors on whatever geometry you choose.
Similar to the hopping terms, you’ll have to decompose pairing terms into strings of Cdagup & Cup and Cdagdn & Cdn. You can see all the pre-defined operators OpSum will recognize here: ITensors.jl/src/lib/SiteTypes/src/sitetypes/electron.jl at main · ITensor/ITensors.jl · GitHub
There is also a 2D hubbard model example to get you started: ITensors.jl/src/lib/ITensorMPS/examples/dmrg/2d_hubbard_conserve_particles.jl at main · ITensor/ITensors.jl · GitHub
Some other things you can do, is once you have written your Hamiltonian you can run a small number of sites and compare with ED/analytical solutions for the non-interacting Hamiltonian to check that its implemented correctly.
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