[aoymt]

Fixes #123.

Summary

With [parameter.simple_update] gauge_fix = true, a bond with fewer nonzero Schmidt values than its dimension filled the tensors with NaN, and the run ended in the environment update with a BLAS error (exit 255). A product initial state without noise is enough.

Input	Before	After
The input of #123 (Heisenberg, Neel state, noise = 0.0)	exit 255	-0.656470
The same with gauge_fix = false	-0.656471	unchanged
The same with noise = 0.01	-0.656469397980045777	the same to all digits
Decoupled dimers at beta = 1, gauge_fix = true, lambda_cutoff = 1e-7	exit 255	exact (-0.124700)

Cause

fix_local_gauge (src/iTPS/core/local_gauge.cpp) diagonalizes the boundary tensors of the two ends of a bond and divides by the square roots of their eigenvalues. boundary_tensor takes the inverse of a lambda below lambda_cutoff for zero, so on a rank-deficient bond the boundary tensors have zero eigenvalues. They come out of eigh as a round-off of either sign: 1 / sqrt(0) is inf, and the square root of a negative one is NaN.

Changes

• A square root at or below lambda_cutoff times the largest is taken for zero, and its inverse too, as is done for lambda.
• The same function tested lambda1[connect2] against the cutoff and inverted lambda2[connect2]. It tests lambda2 now.

Both are needed: with the first change alone, the two cases of the new test still end with exit 255.

Relation to #121

With lambda_cutoff at its present default, 1e-12, the dimers do not show this. A numerically zero lambda of about 1e-8 is then inverted, and the eigenvalue is not zero. Raising the default to 1e-7 (#121) is what makes them crash.

This should be merged before #121, or together with it. Otherwise an input with gauge_fix = true that runs today would stop running.

The four open branches (#120, #121, the version one and this one) merge without conflicts, and the test suite passes on the result (83/83).

Tests

• New: gauge_fix_rank_deficient, an end-to-end test with two cases.
  • The Heisenberg antiferromagnet from the Neel state without noise: the energy must be that of the same run without gauge fixing.
  • Decoupled dimers at a finite temperature with lambda_cutoff = 1e-7: against the exact energy.
• Both cases fail with a build of develop.
• ctest: 78/78 (Apple clang, no MPI, Release).

gauge_fix is off by default, and no input under sample/ or test/ turned it on before this test.

Not tested: an MPI build.

🤖 Generated with Claude Code

[yomichi]

Thanks for the quick fix. I built c33d165 and checked gauge_fix_rank_deficient with mutations:

• the lambda1/lambda2 fix undone: both cases exit with 255,
• the former loop (no sign guard, no cutoff) with the lambda2 fix kept: both cases exit with 255,
• unmodified: both pass, and the Neel energies with and without gauge fixing agree to 1.4e-6.

So both changes are needed, as you say. I also merged #121 into it: gauge_fix_rank_deficient, rank_deficient_bond and test_input pass.

Two small notes, no change needed for this PR:

• The relative cutoff in sqrt_and_inverse is not exercised by the test. I counted what it sets to zero: 600 values in the Neel case and 180000 in the dimers, all from eigenvalues that were zero or negative, none positive. With the cutoff removed (and the sign guard kept), the test still passes. Keeping it is right for a positive round-off eigenvalue; it is just not pinned.
• Nit: the comment in neel() says "1e-6 here", and the tolerance is 1e-4.