Ensuring SU2 with Lagrange Multiplier speed up convergence?

[swanchristmas]

I’m working with a U(1) quantum number conserving system at total S^z=0 and aim to further restrict the state to the singlet sector. Since the non-abelian version is still in development, I am using a Lagrange multiplier approach as follows:

# S² = Sx² + Sy² + Sz²
function Sxy_tot(sites)
    # Effectively, [∑ᵢ(S⁺ᵢ + S⁻ᵢ)/2]² only contribute the cross terms conserving sz.
    os = OpSum()
    for i in eachindex(sites), j in eachindex(sites)
        os += 0.5, "Sp", i, "Sm", j
        os += 0.5, "Sm", i, "Sp", j
    end
    return MPO(os, sites)
end
S2_LM = 100*Sxy_tot(siteinds(ψ))
dmrg([H, S2_LM], ψ; nsweeps, maxdim, cutoff)

Given that the ground state is guaranteed to be a singlet, will introducing this Lagrange multiplier help speed up the convergence? Any comments will be appreciated.

[miles]

I can see why you would ask, but the answer is no. The speedup due to conserving non-Abelian symmetries comes from additional compression of the individual tensors. Here that additional compression will not happen, plus if anything the extra Lagrange multiplier may actually increase the work the computer will need to do a little bit.

I’ve done an approach like this before, though, and it can work well if you do need to obtain eg a singlet state for some other reason.