Emergent de Sitter Space and Non-Unitary Tensor Networks from Non-Hermitian Quantum Criticality
Abstract
Extending the holographic principle to de Sitter (dS) spacetimes remains one of the most vital open frontiers in quantum gravity, where a microscopic, bottom-up tensor-network framework that relates boundary quantum data to emergent de Sitter spacetime is still lacking. In this work, we first show the emergence of de Sitter spacetime from boundary entanglement by formulating a non-unitary continuous multi-scale entanglement renormalization ansatz (cMERA) for a concrete non-Hermitian critical fermion chain. Within this emergent spacetime, we analyze the associated geodesics and show that they act as extremal Ryu-Takayanagi (RT) surfaces undergoing a smooth timelike-to-null transition. Remarkably, we demonstrate that this continuum trajectory suggests a distinct tensor-network architecture in which the bond-counting contribution naturally truncates at the discrete timelike-to-null transition toward the deep infrared. In the resulting architecture, the null ray along the horizon is represented by zero-cost links, since the associated cut severs no tensor legs. This network structure successfully reproduces the logarithmic scaling of non-unitary critical entanglement entropy, offering a bond-counting picture for the de Sitter RT formula. Our results provide the long-sought dS/(c)MERA correspondence at the level of both emergent spacetime and discrete holographic entanglement.
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BibTeX
@misc{chou2026emergent,
title = {{Emergent de Sitter Space and Non-Unitary Tensor Networks from Non-Hermitian Quantum Criticality}},
author = {Kuang-Hung Chou and Po-Yao Chang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.17983},
eprint = {2606.17983},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17983},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emergent de Sitter Space and Non-Unitary Tensor Networks from Non-Hermitian Quantum Criticality
AU - Kuang-Hung Chou
AU - Po-Yao Chang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.17983
UR - https://arxiv.org/abs/2606.17983
AB - Extending the holographic principle to de Sitter (dS) spacetimes remains one of the most vital open frontiers in quantum gravity, where a microscopic, bottom-up tensor-network framework that relates boundary quantum data to emergent de Sitter spacetime is still lacking. In this work, we first show the emergence of de Sitter spacetime from boundary entanglement by formulating a non-unitary continuous multi-scale entanglement renormalization ansatz (cMERA) for a concrete non-Hermitian critical fermion chain. Within this emergent spacetime, we analyze the associated geodesics and show that they act as extremal Ryu-Takayanagi (RT) surfaces undergoing a smooth timelike-to-null transition. Remarkably, we demonstrate that this continuum trajectory suggests a distinct tensor-network architecture in which the bond-counting contribution naturally truncates at the discrete timelike-to-null transition toward the deep infrared. In the resulting architecture, the null ray along the horizon is represented by zero-cost links, since the associated cut severs no tensor legs. This network structure successfully reproduces the logarithmic scaling of non-unitary critical entanglement entropy, offering a bond-counting picture for the de Sitter RT formula. Our results provide the long-sought dS/(c)MERA correspondence at the level of both emergent spacetime and discrete holographic entanglement.
ER -