Planar automatic differentiation.

[Gertian]

I tried to use @lkdvos his new https://github.com/Jutho/TensorKit.jl/tree/ld/planar-ad to get the automatic derivative of the planar PEPS implementation but this seems to fail.

More specifically the /examples/fermionic.jl file fails to execute due to a space mismatch whilst calculating the derivative :

Please note that this is still with ComplexSpaces, the only fermionic part of the code is my usage of @planar and tau symbols.

Edit : my branch is at https://github.com/quantumghent/PEPSKit.jl/tree/planar_branch

[lkdvos]

Could you also include what you ran?

[Gertian]

This file : https://github.com/quantumghent/PEPSKit.jl/blob/planar_branch/examples/fermionic.jl

It's mostly the old testfile from the square lattice Heisenberg. The error comes at line 103 : cfun((ψ₀, env₀)) where

function cfun(x)
    (ψ, env) = x

    function fun(peps)
        env = leading_boundary(peps, alg_ctm, env)
        x = H_expectation_value(peps, env, SqLatHeisenberg())
        return x
    end

    env = leading_boundary(ψ, alg_ctm, env)
    E = H_expectation_value(ψ, env, SqLatHeisenberg())
    ∂E = fun'(ψ)
    @assert !isnan(norm(∂E))    
    return E, ∂E
end

Note that

function H_expectation_value(ψ::InfinitePEPS, env::PEPSKit.CTMRGEnv, H::AbstractTensorMap{S,2,2}) where {S}
    E = 0.0
    for r in 1:size(ψ, 1), c in 1:size(ψ, 2)
        ρ₂ = PEPSKit.ρ₂_horizontal(r, c, ψ, env)

        @planar norm_state = ρ₂[1 2; 1 2]
        @planar energy_horizonal = H[1 3; 2 4] * ρ₂[2 4; 1 3]

        E = E + (energy_horizonal*(-1)^r )/norm_state
    end
    if !(E ≈ real(E)) 
        @warn "Zygote seems to manage to generate a state for which the energy is infinite. This is not good."
        @show E 
    end
    return real(E)
end

returns real(E) if not zygote stalls earlier because it seems to find a state with E = inf + im*inf that then triggers an error in gradient calculation because it's doesn't want to calculate gradients of complex functions.

[lkdvos]

Ok I'm a bit confused about why it works at all now, I haven't actually implemented any traces at all, so the 6th line of your expectation value shouldn't be working :p

[Gertian]

It's already failing when taking the derivative of the 4th line.

[lkdvos]

yes, but it should be deriving things backwards, so the 6th line comes first 🙃

[Gertian]

Ok, fair enough 😅

Then this is the first contraction it's coming across that contains tau symbols

[lkdvos]

Will close this issue for now, the fermions should be supported, and I don't think there are too many plans to support anyonic systems in the near future.