feat(ipeps): split_honeycomb_merge — SVD reverse of Honeycomb A/B merge

[yuchihe]

Summary

Add split_honeycomb_merge(M; convention, χmax, cutoff) in
src/ipeps_optimize/build_A.jl — the inverse of the Honeycomb sublattice
merge. Given a merged single-site iPEPS tensor M of shape
(D, D, D, D, d²), it returns two sublattice tensors A and B with
three virtual legs and one physical leg each, joined by a new internal
virtual bond of dimension χ ≤ D²·d produced by a single SVD.

Details

• Reshape physical leg σ_AB to (σ_A, σ_B) in Julia's column-major
  order (σ_A is the inner index).
• Permute legs into an (A-side | B-side) grouping selected by the
  convention keyword:
  • :LU_RD (default, "anti-diagonal" merge): A keeps (L, U),
    B keeps (R, D). Reconstruction
    M[L,D,R,U,σ_AB] = Σ_x A[L,U,σ_A,x] · B[x,R,D,σ_B].
    This matches the natural u/v merge along the a bond in the
    brickwall convention (u with external (L=c, U=b), v with
    external (R=c, D=b)).
  • :LD_RU ("diagonal" merge): A keeps (L, D), B keeps (R, U).
• SVD on the (D²d × D²d) matrix, distribute singular values evenly
  between A and B (A·√S and √S·B').
• χmax > 0 caps the bond; cutoff > 0 discards S[i] ≤ cutoff · S[1].

Returns a NamedTuple (A, B, S):

• A: shape (D, D, d, χ) — A[extA1, extA2, σ_A, x_internal]
• B: shape (χ, D, D, d) — B[x_internal, extB1, extB2, σ_B]
• S: kept singular values (length χ)

Test plan

Added a @testset "split_honeycomb_merge SVD reverse" block in
test/test_ipeps.jl that:

• Builds random A, B with χ = D²d, contracts to form M, calls
  split_honeycomb_merge, and verifies M_reconstructed ≈ M for
  both :LU_RD and :LD_RU conventions.
• Checks output shapes: A is (D, D, d, D²d), B is (D²d, D, D, d),
  length(S) == D²d.
• Verifies χmax = 5 keeps exactly 5 singular values (largest) and
  that the returned S is sorted in descending order.
• Verifies ArgumentError is thrown for non-square physical dim,
  mismatched virtual bond dims, and unknown convention symbol.

🤖 Generated with Claude Code