Beyond Calabrese-Cardy Scaling: Exceptional-Point Sensitivity and the de Sitter RT Surface
Abstract
Entanglement entropy at one-dimensional criticality typically follows the Calabrese--Cardy scaling. In the non-Hermitian critical free-fermion systems studied here, however, we find an additional interval-independent contribution Sres=log(ΔL), which allows the entropy to remain sensitive to energy gaps below the finite-size scale, Δ<1/L. We refer to this term as the residual entropy. To understand its infrared origin, we examine finite-depth non-unitary continuous multiscale entanglement renormalization on a ring. Terminating the critical RG circuit before its singular final layer leaves a two-site infrared state. We calculate the entropy of this state directly from its correlation matrix and recover the same log(ΔL) dependence. The emergent de Sitter geometry provides a complementary geometric interpretation: extremal curves associated with different boundary intervals extend to a common infrared endpoint, suggesting how the entanglement retained there can contribute equally to their entropies.
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BibTeX
@misc{chou2026beyond,
title = {{Beyond Calabrese-Cardy Scaling: Exceptional-Point Sensitivity and the de Sitter RT Surface}},
author = {Kuang-Hung Chou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.21536},
eprint = {2607.21536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21536},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond Calabrese-Cardy Scaling: Exceptional-Point Sensitivity and the de Sitter RT Surface
AU - Kuang-Hung Chou
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2607.21536
UR - https://arxiv.org/abs/2607.21536
AB - Entanglement entropy at one-dimensional criticality typically follows the Calabrese--Cardy scaling. In the non-Hermitian critical free-fermion systems studied here, however, we find an additional interval-independent contribution S_res=log(ΔL), which allows the entropy to remain sensitive to energy gaps below the finite-size scale, Δ<1/L. We refer to this term as the residual entropy. To understand its infrared origin, we examine finite-depth non-unitary continuous multiscale entanglement renormalization on a ring. Terminating the critical RG circuit before its singular final layer leaves a two-site infrared state. We calculate the entropy of this state directly from its correlation matrix and recover the same log(ΔL) dependence. The emergent de Sitter geometry provides a complementary geometric interpretation: extremal curves associated with different boundary intervals extend to a common infrared endpoint, suggesting how the entanglement retained there can contribute equally to their entropies.
ER -