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Fix the global sign of the C4v corner spectrum for convergence - #436
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Oof! Sorry that I introduced this bug, I should indeed have thought of this. Modulo one small performance question LGTM |
The C4v convergence check compares corner eigenvalues, so a fixed point on which every iteration maps (C, E) to (-C, -E) never registered as converged. Fix the sign of the spectrum such that the eigenvalue of largest magnitude is positive.
Co-authored-by: Katharine Hyatt <kshyatt@users.noreply.github.com>
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Since #419, C4v CTMRG measures corner convergence through the eigenvalue spectrum of the corner (
eigh_vals) instead of its singular values. Some fixed points are only fixed up to a sign: every iteration maps(C, E)to(-C, -E). The edge spectrum (singular values) does not see that sign, but the corner eigenvalues flip with it, so their distance to the previous iteration stays finite and CTMRG runs untilmaxiterwithout reporting convergence.This happens, for instance, for states with half-integer U(1) charges on the virtual bonds, where fixed points come in pairs, one of which flips sign every iteration. Starting from a random environment, CTMRG can land on either.
This PR fixes the global sign of the C4v corner spectrum such that the eigenvalue of largest magnitude is positive, so that the spectra of
Cand-Ccoincide. Unlike comparing absolute values, as the singular values did before #419, this still detects eigenvalues that change sign relative to the others.The new test
test/ctmrg/c4v_sign_branches.jlconverges a half-integer U(1) Heisenberg state, constructs the twin of its fixed point, checks that the two branches have opposite iteration signs, and checks that CTMRG converges on both to the same energy.