Mixed-site (Boson,spin) model

[Ashinxinl]

Hi,

Thanks for your support so far! I have a question about creating a mixed site set involving spin and bosons。I have recently started learning physics and ITensor, so I have limited understanding of how to represent mixed-type MPOs (Matrix Product Operators). Could you provide me with some guidance or suggestions to help me better understand and represent these mixed-type MPOs?

Thanks again for everything! I really appreciate it.

[miles]

You can make Hamiltonians for “mixed” Hilbert space types by following similar steps to the Code Example in the documentation at this link:
https://itensor.github.io/ITensors.jl/dev/examples/DMRG.html#DMRG-Calculation-with-Mixed-Local-Hilbert-Space-Types

Those steps are:

1. make a site array that contains site indices of different site types (site types are special Index tags such as “S=1/2” or “Boson” that our system looks for in order to make operators)
2. use our OpSum system to make your Hamiltonian, and input appropriate strings of operators that you want to make or include in the sum

For your example, you can do something like

sites = siteinds(n->isodd(n) ? "Boson" : "S=1/2",N)

terms = OpSum()
for i=1:2:N
#...
terms += -alpha, "Adag",i,"Z",i+1,"A",i+2
terms += -alpha, "A",i,"Z",i+1,"Adag",i+2

#...
end

where I’ve made some slightly different choices than in your math above, the main one being that I’ve made the spins live on different sites than the bosons, instead of in your math where you treat them as living on the same site. (Both are mathematically ok, but it’s practically more convenient and efficient in DMRG / MPS methods to split them across different sites.)

Finally, please note that if you use “Boson” sites in ITensorMPS, that they come with a default maximum occupancy. If you need a larger occupancy for your system you should increase it.

You can also make site arrays in a more “manual” way by making the site indices one-by-one in a loop and push! -ing them into an array, which lets you control more easily the details of each site index.

[Ashinxinl]

Thank you for your patient and detailed response; it was very helpful to me. Wishing you a happy life!