MPO for number operators and the calculation of correlation function in VUMPS

ITensor Julia Questions
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1

Hi Matt,

I have been trying to define the MPO for electron number operators following the definition of the Hamiltonian MPO:

function ITensorInfiniteMPS.unit_cell_terms(::Model"eNumber")
  opsum = OpSum()
  opsum += "Ntot", 1
  return opsum
end													

NumberOp = InfiniteSum{MPO}(Model("eNumber"), s)

However, I got the error “LoadError: MethodError: no method matching translatecell(::ITensorInfiniteMPS.var”#_shift_cell#149"{Int64}, ::Scaled{ComplexF64, Prod{Op}}, ::Int64)".

Another related question is how do we calculate the electron correlation functions in VUMPS? Is there a documentation or example that I could refer to?

Thanks again for your time,
-Meng

2

Hi Meng-Zeng,

I also would like to calculate correlation functions by VUMPS. Any insights on that? Or do you find any references?

Best,
Feng

3

This example includes computing a correlation matrix by slicing an infinite MPS to a finite MPS and computing the correlation matrix of that slice with ITensors.jl: https://github.com/ITensor/ITensorInfiniteMPS.jl/blob/main/examples/vumps/vumps_hubbard_extended.jl

@Meng-Zeng could you show a complete runnable example? For example, you don’t show what s is.

4

Hi everyone.

@mtfishman Not sure if I should make a new question, but this error is exactly what I get when I try to construct the infinite MPO for a Hamiltonian of a custom model. Here is a runnable example.

m2= 10
ld =1


maxdim = 100 # Maximum bond dimension
cutoff = 1e-8 # Singular value cutoff when increasing the bond dimension
max_vumps_iters = 100 # Maximum number of iterations of the VUMPS algorithm at each bond dimension
vumps_tol = 1e-6
conserve_qns = false
outer_iters = 8 # Number of times to increase the bond dimension


N = 10 # Number of sites in the unit cell

initstate(n) = isodd(n) ? "1" : "2"
s = infsiteinds("Boson", N; dim=8, conserve_qns, initstate)
ψ = InfMPS(s, initstate)

model = Model("Realphi4")

# Form the Hamiltonian
H = InfiniteSum{MPO}(model, s)

Where the “Realphi4” model is

function ITensorInfiniteMPS.unit_cell_terms(::Model"Realphi4")
    opsum = OpSum()
    opsum += 0.5, "cpi2",1
    opsum += 0.5*(1+m2), "phi",1,"phi",1
    opsum += 0.5, "phi",2,"phi",2
    opsum += -1, "phi",1,"phi",2
    opsum += ld/24 ,"phi",1,"phi",1,"phi",1,"phi",1
    return opsum
end

where the local custom operators have matrix elements equivilent to superpositions of A and Adag, and their squares.

The error comes from the InfiniteSum. Thanks!

Best,
Jake