# how to construct two component bose hubbard model in Julia Itensor?

**URL:** <https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806>\
**Category:** ITensor Julia Questions\
**Tags:** julia, mps, mpo\
**Created:** [April 25, 2023, 10:21pm UTC](https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806 "2023-04-25T22:21:13Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![Aditya214](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/aditya214/32/231_2.png) [@Aditya214](https://itensor.discourse.group/u/Aditya214)\
**Post date:** [April 25, 2023, 10:21pm UTC](https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806/1 "2023-04-25T22:21:14Z")

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Hello everyone,  
I went through the answers to code 2 component bose Hubbard model in the Itensor C++ version however I was not able to code in the Julia version. Could you please let me know the way to code the following hamiltonian?

 ![image](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/448162672299d4fef3ce22cc32653ce99c8be071.png)

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**Author:** ![JanReimers](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/janreimers/32/171_2.png) [@JanReimers](https://itensor.discourse.group/u/JanReimers)\
**Post date:** [April 25, 2023, 11:45pm UTC](https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806/2 "2023-04-25T23:45:07Z")

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Starting with the C++ code [here](https://itensor.discourse.group/t/how-to-construct-a-one-dimensional-two-component-bose-hubbard-model/112) I came up with this:

```auto
using ITensors
function two_component_BH(N::Int64;U=1.0,U12=-0.5,t1=0.5,t2=0.25,kwargs...)
    sites = siteinds("Boson",N;conserve_qns=true,conserve_number=false)
    op = OpSum()
    for i in 1:2:N-3
        op += -U/2, "N", i
        op += U/2, "N", i,"N",i
        op += -t1, "a", i, "a†", i + 2
        op += -t1, "a†", i, "a", i + 2
    end
    op += -U/2, "N", N-1
    op += U/2, "N", N-1,"N",N-1

    for i in 2:2:N-2
        op += -U/2, "N", i
        op += U/2, "N", i,"N",i
        op += -t2, "a", i, "a†", i + 2
        op += -t2, "a†", i, "a", i + 2
    end
    op += -U/2, "N", N
    op += U/2, "N", N,"N",N

    for i in 1:2:N-1
        op +=U12, "N", i,"N",i+1
    end
    MPO(op,sites;kwargs...)
end

two_component_BH(6)

```

Hopefully you can adjust this to meet your needs. ITensors uses “a” and “a†” for bosons, and “c” and “c†” for fermions. There details are [here](https://itensor.github.io/ITensors.jl/stable/IncludedSiteTypes.html#%22Boson%22-SiteType).

Let us know how you make out.  
Kind Regards  
Jan

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**Author:** ![ImVictorCheng](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/imvictorcheng/32/643_2.png) [@ImVictorCheng](https://itensor.discourse.group/u/ImVictorCheng)\
**Post date:** [September 26, 2024, 1:38pm UTC](https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806/3 "2024-09-26T13:38:28Z")

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Hi, I’m working on a similar system and came across your answer. Does your method mean you are treating a\_{j,\up} as a\_{2k} and a\_{j,\down} as a\_{2k+1}? Does this work with situations that involve spin filpping? Thanks!

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**Author:** ![Aditya214](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/aditya214/32/231_2.png) [@Aditya214](https://itensor.discourse.group/u/Aditya214)\
**Post date:** [September 26, 2024, 5:56pm UTC](https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806/4 "2024-09-26T17:56:38Z")

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Hi Victor,  
Yes my method means I am treating a\_{j,\up} as a\_{2k} and a\_{j,\down} as a\_{2k+1}. I am not sure about the spin flipping case, could you elaborate, or mention the hamiltonian you are talking about?

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**Author:** ![ImVictorCheng](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/imvictorcheng/32/643_2.png) [@ImVictorCheng](https://itensor.discourse.group/u/ImVictorCheng)\
**Post date:** [September 27, 2024, 12:49am UTC](https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806/5 "2024-09-27T00:49:44Z")

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Thanks your the reply. In my model, a spin flip would look like a^{\dagger}\_{j\uparrow}a\_{i\downarrow}. Would that simply be a^{\dagger}\_{2j}a\_{2i+1}?

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**Author:** ![Aditya214](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/aditya214/32/231_2.png) [@Aditya214](https://itensor.discourse.group/u/Aditya214)\
**Post date:** [November 21, 2024, 10:54pm UTC](https://itensor.discourse.group/t/how-to-construct-two-component-bose-hubbard-model-in-julia-itensor/806/6 "2024-11-21T22:54:10Z")

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yes, sorry for the late reply.