[osvathbotond]

Description

Fix fourth-order TDVP evolution, which currently throws a BoundsError on the third substep.

sub_time_steps(::TDVPOrder{4}) defines six substeps, but orderings(::TDVPOrder{4}) supplies only two sweep directions. Repeat the forward/reverse direction pair three times to match the three symmetric second-order stages encoded by the existing coefficients.

Minimal demonstration of previous behavior

using ITensors, ITensorMPS

sites = siteinds("S=1/2", 4)
terms = OpSum()
for j in 1:3
    terms += 0.5, "S+", j, "S-", j + 1
    terms += 0.5, "S-", j, "S+", j + 1
    terms += 1.0, "Sz", j, "Sz", j + 1
end
H = MPO(terms, sites)
psi = MPS(sites, ["Up", "Dn", "Up", "Dn"])

psi_evolved = tdvp(H, -0.1im, psi; nsteps=1, order=4, cutoff=1e-12, maxdim=16, outputlevel=0)
# Throws BoundsError when accessing the third sweep direction.

Minimal demonstration of new behavior

using ITensors, ITensorMPS

sites = siteinds("S=1/2", 4)
terms = OpSum()
for j in 1:3
    terms += 0.5, "S+", j, "S-", j + 1
    terms += 0.5, "S-", j, "S+", j + 1
    terms += 1.0, "Sz", j, "Sz", j + 1
end
H = MPO(terms, sites)
psi = MPS(sites, ["Up", "Dn", "Up", "Dn"])

psi_evolved = tdvp(H, -0.1im, psi; nsteps=1, order=4, cutoff=1e-12, maxdim=16, outputlevel=0)
# Successfully returns the evolded MPS.

How Has This Been Tested?

Added test/base/test_solvers/test_tdvp_orders.jl:

• Compare six-site evolution against an independently constructed dense matrix exponential, including the full state and global phase.
• Cover conserved and unconserved quantum numbers, both initial sweep directions, and one-site/two-site updates.
• Verify first-, second-, and fourth-order timestep convergence using successive refinements of a nontrivial fixed-rank, one-site TDVP flow without QN conservation.
• Check norm conservation and stability under tighter local-solver tolerance.

All 136 assertions passed locally on Julia 1.13.0 after formatting:

• 62 dense-exponential accuracy assertions.
• 74 timestep-convergence assertions.

Formatter idempotence was also verified. The full repository test suite has not been run locally.

Checklist

• My code follows the style guidelines of this project. Ran ITensorFormatter v0.2.30 on both changed files.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have added tests that verify the behavior of the changes I made.
• I have made corresponding changes to the documentation. Not applicable: this restores existing behavior without changing the API.
• My changes generate no new warnings. The same dependency/import warnings appeared before and after formatting; an unmodified-upstream baseline has not been checked.
• Any dependent changes have been merged and published in downstream modules. Not applicable: no dependent changes are required.