MPO for an exponential operator

ITensor Julia Questions
1

I am trying to define the MPO for the operator exp(i theta n_j) for the Anyon Hubbard model(mapped to an interacting boson model). I have tried to define an operator using the op function for the matrix of exp(i theta n_j) and then use it in the operator sum for the Hamiltonian but am recieving a method error in trying to do so.

image

(ImageSource:DOI: 10.1038/ncomms1353)

function Ham(θ,N,d)
    s = siteind("Qudit",dim=d)
    function expnmat(θ, d)
        return [(i == j) ?  exp(1im*θ*(i-1)) : 0.0 for i in 1:d, j in 1:d]
    end
    
    statphase = op(expnmat(θ,d), s)
    
    
    sites = siteinds("Qudit",N,conserve_qns=true,dim=d)
    os = OpSum()
    for j=1:N-1
    os += ("adag",j,"a",j+1,"statphase",j)
    os += ("statphase",j,"adag",j+1,"a",j)
    os += 1/2,"n",j, "n",j
    os -= 1/2,"n",j    
    end
    H = MPO(os,sites)
    return H 
end
1 Like
2

To make a new operator definition that OpSum will recognize, you will need to make a new overload of the ITensors.op method. Please see the code examples and walkthrough in the documentation here:
https://itensor.github.io/ITensors.jl/dev/examples/Physics.html#custom_op

And let us know if you have any questions about that process.

3

I am also experiencing this problem. Has it been resolved? My computer skills are quite low

4

Hi, Ashinxinl could you please start a new topic with details about what problem you are encountering (the original post above was pretty vague about what the error was), and also share what error message or incorrect output you are getting? Thanks –