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arXiv:2606.17983

Emergent de Sitter Space and Non-Unitary Tensor Networks from Non-Hermitian Quantum Criticality

Kuang-Hung Chou, Po-Yao Chang

quant-phcond-mat.stat-mechhep-thSubmitted Jun 16, 2026• Announced Jun 17, 2026• 0 citations
v1 · Jun 16, 2026v2 · Sep 30, 2026
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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 dictates 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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13 pages, 4 figures

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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 dictates 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.
Standard Ryu-Takayanagi (RT) bounds and Multiscale Entanglement Renormalization Ansatz (MERA) networks assume a costless, unitary mapping between continuous bulk geometry and discrete boundary information. In this Letter, we show that projecting continuous bulk fields into discrete boundary states introduces a mandatory topological phase-space friction governed by the Euler-Mascheroni constant γ\gammaγ. Normalizing this harmonic discretization residue across the geometric capacity of a two-dimensional boundary yields the exact holographic delamination invariant, Λ2=exp⁡(γ/π2)≈1.060228\Lambda_2 = \exp(\gamma/\pi^2) \approx 1.060228Λ2​=exp(γ/π2)≈1.060228. By demonstrating that discrete MERA layer scaling is the exact mathematical dual to the logarithmic AdS radial measure, we prove this additive topological penalty exponentiates into a strict multiplicative scaling of thermodynamic work. We construct non-unitary dissipative MERA disentangler operators (Υ^\hat{\Upsilon}Υ^) that enforce a factorization bound on accessible boundary entropy SaccS_{\text{acc}}Sacc​. Acting as a covariant topological scalar, this invariant preserves the Equivalence Principle while establishing a fundamental thermodynamic and semantic limit on holographic state projection.
Holographic tensor networks serve as toy models for the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, capturing many of its essential features in a concrete manner. However, existing holographic tensor network models remain far from a complete theory of quantum gravity. A key obstacle is their discrete structure, which only approximates the semi-classical geometry of gravity in a qualitative sense. In \cite{Lin:2024dho}, it was shown that a network of partial-entanglement-entropy (PEE) threads, which are bulk geodesics with a specific density distribution, generates a perfect tessellation of AdS space. Moreover, such PEE-network tessellations can be constructed for more highly symmetric geometries using the Crofton formula. In this paper, we assign a quantum state to each vertex in the PEE network and develop several holographic tensor network models: (1) the factorized PEE tensor network, which takes the form of a tensor product of EPR pairs; (2) the HaPPY-like PEE tensor network constructed from perfect tensors; and (3) the random PEE tensor network. In all these models, we reproduce the exact Ryu-Takayanagi formula by showing that the minimal number of cuts along a homologous surface in the network exactly equals the area of that surface.
This study extends the framework of non-equilibrium Hamiltonian field theory and algebraic coset partitioning established in preceding architectures to holographic quantum information manifold sectors, providing an explicit formulation for the macroscopic emergence of anti-de Sitter (AdS) spacetimes driven by the variational minimization of codimension-two entangling surfaces inside boundary conformal field theories (CFT). By embedding the Helfrich elastic bending grammar into the generalized Ryu-Takayanagi entropy functional, the spontaneous emergence of localized bulk horizons coupled to quantum error-correcting stabilizer codes is formalized. Partitioning the total configuration space under tensor network constraints demonstrates that non-local entanglement geometries undergo algebraic degeneration into exactly three universal holographic cosets.
The AdS/CFT correspondence conjectures a duality between quantum gravity theories in anti-de Sitter (AdS) spacetime and conformal field theories (CFTs) on the boundary. One intriguing aspect of this correspondence is that it offers a pathway to explore quantum gravity through tabletop experiments. Recently, a multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT that can be implemented using contemporary quantum simulators has been proposed [R. Sahay, M. D. Lukin, and J. Cotler, arXiv:2401.13595 (2024)]. Particularly, local bulk excitations (entitled "hologrons") manifesting attractive interactions given by AdS gravity were found. However, the fundamental question concerning the stability of these identified hologrons is still left open. Here, we address this question and find that hologrons are unstable during dynamic evolution. In searching for stable bulk excitations with attractive interactions, we find they can be constructed by the local primary operators in the boundary CFT. Furthermore, we identify a class of boundary excitations that exhibit the bizarre behavior of "holographic transportation", which can be directly observed on the boundary system implemented in experiments.
A bstract We provide a derivation of the Ryu-Takayanagi (RT) formula in 3D gravity for generic boundary subregions — including RT surface phase transitions — directly from the dual two-dimensional conformal field theory (CFT). Our approach relies on the universal statistics of the algebraic conformal data and the large- c behavior of conformal blocks with Cardy boundaries involved. We observe the emergence of 3D multi-boundary black holes with Karch-Randall branes from entangled states of any number of CFTs with and without Cardy boundaries. The RT formula is obtained directly from the CFT in the high-temperature regime. Two direct applications are: 1) A simple derivation of the multi-interval entanglement entropy for the vacuum state of a single CFT; 2) A CFT-based detection of the emergence of replica wormholes in the context of entanglement islands and black hole microstate counting. Our framework yields the first holographic random tensor network that faithfully captures the entanglement structure of holographic CFTs. These results imply that bulk spacetime geometries indeed emerge from the eigenstate thermalization hypothesis (ETH) in the dual field theory in the large- c limit — a paradigm we refer to as It from ETH .
Recent advances have suggested that spacetime itself emerges from the entanglement of the quantum degrees of freedom living on the boundary. In the case of the anti-de Sitter (AdS) spacetimes, a particular class of tensor networks has been shown to realize the same via Multi-Scale Entanglement Renormalization Ansatz (MERA). In this paper, we suggest a prescription for the dS/MERA correspondence and recover a discrete version of dS Penrose diagram by using the MERA on conformal theories identified with the future/past boundaries ([Formula: see text]) of the dS spacetime. In this case, as anticipated, time appears as the emergent direction. We comment on the possible interpretation that the dS cosmological horizon entropy involves entanglement with degrees of freedom across the cosmological horizon as well as the implications of our construction for cosmology.