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arXiv · 2607.21536

Beyond Calabrese-Cardy Scaling: Exceptional-Point Sensitivity from the de Sitter RT Surface

Kuang-Hung Chou
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Abstract

Entanglement entropy at one-dimensional criticality typically follows the Calabrese-Cardy scaling. In non-Hermitian critical chains near exceptional points, however, we show that the biorthogonal entropy of a finite system retains an additional sensitivity to a small energy gap \(\Delta\) even when \(\Delta < 1/L\). On top of the usual Calabrese-Cardy term, we find an interval-independent contribution \(S_{\rm res}=\log(\Delta L)\), visible as a vertical offset and detectable even for a one-site subsystem. This behavior has no Hermitian analogue: a sub-finite-size gap is effectively invisible to entanglement in unitary critical chains, whereas here the entropy continues to resolve such a gap through its dependence on \(\Delta L\). We interpret the result within the de Sitter geometry generated by non-unitary continuous multiscale entanglement renormalization: because the dS extremal surface reaches the IR endpoint, entanglement necessarily retains the endpoint contribution. On a finite ring, a regular circuit cannot terminate at a one-site product state and instead leaves an entangled two-site IR state. Computing the entanglement of the IR state recovers the same \(\log(\Delta L)\) term, identifying this additional long-range entanglement as the residual entropy left after finite-depth disentangling.

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Kuang-Hung Chou. 2026-07-23. Beyond Calabrese-Cardy Scaling: Exceptional-Point Sensitivity from the de Sitter RT Surface. https://arxiv.org/abs/2607.21536

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