Add quantum Ashkin-Teller model

[BramVancraeynest]

Add quantum Ashkin-Teller model to MPSKitModels.jl.
Currently only implemented with Z2Irrep ⊠ Z2Irrep symmetry. I've added one test that checks for a number of parameters for which the model is dual to the spin 1/2 XXZ chain, and thus integrable, the ground state energy density.

[lkdvos]

Thanks for this! Out of curiosity, would it help you/make this kind of model easier to implement for arbitrary symmetries if we include a function for blocking sites?
I don't know that much about this model, but it looks to me like it could be realized with the deligneproduct from TensorKit, which works on tensors as well (somewhat not well-known feature)

[codecov]

Codecov Report

❌ Patch coverage is 81.81818% with 6 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/models/hamiltonians.jl	84.37%	5 Missing ⚠️
src/utility.jl	0.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/MPSKitModels.jl	100.00% <ø> (ø)
src/utility.jl	55.55% <0.00%> (-3.27%)	⬇️
src/models/hamiltonians.jl	47.50% <84.37%> (+9.21%)	⬆️

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[BramVancraeynest]

Thanks for this! Out of curiosity, would it help you/make this kind of model easier to implement for arbitrary symmetries if we include a function for blocking sites? I don't know that much about this model, but it looks to me like it could be realized with the deligneproduct from TensorKit, which works on tensors as well (somewhat not well-known feature)

Yes, initially I was indeed trying to construct the local Hamiltonian terms with the deligneproduct implementation for TensorMaps before resorting to the current implementation. I agree that such an implementation would probably be preferable.
As far as I can tell, after invoking the deligneproduct for the on-site (nearest-neighbour) terms, this requires to fuse the (co)domain so as to obtain a rank 2 (rank 4) tensor? For the on-site operators something like:

using TensorKit

T = ComplexF64
S = Z2Irrep ⊠ Z2Irrep
V = Vect[S](c => 1 for c in values(S))

X = σˣ(T, Z2Irrep)
Id = one(X)

f = isometry(T, V, codomain(Id ⊠ Id))

@tensor XI[-1; -2] := f[-1; 1 2] * (X ⊠ Id)[1 2; 3 4] * conj(f[-2; 3 4])
@tensor IX[-1; -2] := f[-1; 1 2] * (Id ⊠ X)[1 2; 3 4] * conj(f[-2; 3 4])
@tensor XX[-1; -2] := f[-1; 1 2] * (X ⊠ X)[1 2; 3 4] * conj(f[-2; 3 4])

[lkdvos]

Sorry for taking a while to get to this, I made some small changes which I think makes it so it automatically works with a variety of symmetries, for most cases except for the additional Z2 you would have for interchanging the two Z2s, for which I am not convinced it actually leads to a speedup anyways.
Let me know what you think, I'll try and merge + tag something tomorrow.

[BramVancraeynest]

Thanks so much! Looks great!