PEPSKit 0.6.0: LAPACK error and CTMRG failure in Fermi-Hubbard example with symmetries

[DaanVrancken]

Hi all!

Since I started using the new 0.6.0 version of PEPSKit, I have encountered some issues which were not there before. It might be easiest to illustrate using the example of the Fermi-Hubbard model.

So everything starts out fine

using Random
using TensorKit, PEPSKit
using MPSKit: add_physical_charge
Random.seed!(2928528937);

t = 1.0
U = 8.0
lattice = InfiniteSquare(2, 2);

fermion = fℤ₂
particle_symmetry = U1Irrep
spin_symmetry = Trivial
S = fermion ⊠ particle_symmetry

D, χ = 1, 1
V_peps = Vect[S]((0, 0) => 2 * D, (1, 1) => D, (1, -1) => D)
V_env = Vect[S](
    (0, 0) => 4 * χ, (1, -1) => 2 * χ, (1, 1) => 2 * χ, (0, 2) => χ, (0, -2) => χ
)
S_aux = S((1, -1))
H₀ = hubbard_model(ComplexF64, particle_symmetry, spin_symmetry, lattice; t, U)
H = add_physical_charge(H₀, fill(S_aux, size(H₀.lattice)...));

boundary_alg = (; tol=1e-8, alg=:simultaneous, trscheme=(; alg=:fixedspace))
gradient_alg = (; tol=1e-6, alg=:eigsolver, maxiter=10, iterscheme=:diffgauge)
optimizer_alg = (; tol=1e-4, alg=:lbfgs, maxiter=80, ls_maxiter=3, ls_maxfg=3)

But when looking for env₀

physical_spaces = physicalspace(H)
virtual_spaces = fill(V_peps, size(lattice)...)
peps₀ = InfinitePEPS(randn, ComplexF64, physical_spaces, virtual_spaces)
env₀, = leading_boundary(CTMRGEnv(peps₀, V_env), peps₀; boundary_alg...);

CTMRG does not converge and the obj goes to some extremely small value:

[ Info: CTMRG init:     obj = -1.173626607429e+01 -1.256545451178e+01im err = 1.0000e+00
┌ Warning: CTMRG cancel 100:    obj = +1.059865706798e-167      err = 1.4137871225e+00  time = 28.30 sec
└ @ PEPSKit C:\Users\dvrancke\.julia\packages\PEPSKit\2FBaz\src\algorithms\ctmrg\ctmrg.jl:155

When trying to find the ground state anyway

peps, env, E, info = fixedpoint(
           H, peps₀, env₀; boundary_alg, gradient_alg, optimizer_alg, verbosity=3
       )

this results in a LAPACK error.

I have also encountered this for other fermionic models using symmetries. Also, when trying to do simple update, it "converges" after the first iteration, whereas this used to work well with previous versions. Any idea what could be wrong?

[GlebFedorovich]

Hi Daan!
From my experience, unless you environment is converged enough, further AD optimization is not stable at all, so, LAPACK errors are one of the symptoms. Have you tried to shuffle the dimensions of sectors in your virtual space? One thing that might help is also at first run leading_boundary with trsheme = truncdim(chi_total) for 10-20 iterations, take the output environment and later put it as input for leading_boundary with trsheme = FixedSpaceTruncation()

P.s. or did you env converge well with the same code for 0.5.0 version?

[DaanVrancken]

Hi Gleb!
Thanks for the quick response. I could certainly try this, but yes: this used to work well with 0.5.0.

[lkdvos]

Hi Daan, sorry for taking a while to figure this out, just summarizing the fix: we altered the convention of the add_physical_charge function, so really you should be adding S((1, 1)) instead. This was definitely something that was a weird convention before, but you do need to update existing scripts to account for this.

[DaanVrancken]

Thanks, that indeed fixes the problem!