超越卡拉布雷塞 - 卡迪标度：德西特RT曲面的例外点敏感性
Beyond Calabrese-Cardy Scaling: Exceptional-Point Sensitivity from the de Sitter RT Surface
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中文总结 AI 辅助
研究非厄米临界链靠近例外点时的纠缠熵，发现双正交熵对小能隙\(\Delta\)有额外敏感性，存在与区间无关的\(S_{\rm res}=\log(\Delta L)\)贡献，通过德西特几何解释，揭示了额外长程纠缠即残余熵。
中文摘要 AI 辅助
一维临界性下的纠缠熵通常遵循卡拉布雷塞 - 卡迪标度。然而，在非厄米临界链中靠近例外点时，我们表明即使\(\Delta < 1/L\)，有限系统的双正交熵对小能隙\(\Delta\)仍保留额外敏感性。除了通常的卡拉布雷塞 - 卡迪项，我们发现一个与区间无关的贡献\(S_{\rm res}=\log(\Delta L)\)，表现为垂直偏移且对单点子系统也可检测到。这种行为在厄米系统中无类似情况。我们在非酉连续多尺度纠缠重整化产生的德西特几何中解释该结果，因为德西特极值曲面到达红外端点，纠缠必然保留端点贡献。在有限环上，正则电路不能终止于单点子积态，而是留下纠缠的两体红外态。计算红外态的纠缠恢复相同的\(\log(\Delta L)\)项，将这种额外的长程纠缠识别为有限深度解缠后留下的残余熵。
英文摘要
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 \(Δ\) even when \(Δ< 1/L\). On top of the usual Calabrese-Cardy term, we find an interval-independent contribution \(S_{\rm res}=\log(ΔL)\), 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 \(ΔL\). 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 \(\log(ΔL)\) term, identifying this additional long-range entanglement as the residual entropy left after finite-depth disentangling.
