truncrank with symmetries seems to lead to unbalanced charges #588

using TensorKit, LinearAlgebra, Random
Random.seed!(1)

# blocks have identical singular values up to rounding.
V = U1Space(0 => 2, 1 => 1, -1 => 1)
A = randn(ComplexF64, V ⊗ V ← V ⊗ V)
@tensor T[a1 a2 b1 b2; c1 c2 d1 d2] := A[a1 a2; c1 c2] * conj(A[b1 b2; d1 d2])

_, Sfull, _ = svd_compact(T)
for q in (1, 2)
    Δ = maximum(abs, diag(block(Sfull, U1Irrep(q))) .- diag(block(Sfull, U1Irrep(-q))))
    println("q = ±$q: singular value difference = $Δ")
end

# truncate and figure out if any charges are missing their opposite sign partner(s)
function unbalanced(trunc)
    _, S, _ = svd_trunc(T; trunc)
    W = space(S, 1)
    d = Dict(c.charge => dim(W, c) for c in sectors(W))
    return dim(W), sort([q for q in keys(d) if d[q] != get(d, -q, 0)])
end

for χ in 20:30
    n, bad = unbalanced(truncrank(χ))
    println("truncrank($χ): kept $n, unbalanced charges $bad")
end
n, bad = unbalanced(trunctol(; rtol = 1.0e-2))
println("trunctol(rtol = 1e-2): kept $n, unbalanced charges $bad")