Entanglement Renormalization of Non-Hermitian Systems and the Emergent de Sitter Space

The Ryu-Takayanagi (RT) formula elucidates the fundamental link between bulk spacetime and the entanglement properties of boundary theory. The multi-scale entanglement renormalization ansatz (MERA) provides a concrete framework for demonstrating how the geometry of bulk spacetime arises from the entanglement structure of the boundary. A notable example is the Anti-de Sitter (AdS)/continuous MERA (cMERA) correspondence, particularly realized through cMERA in Hermitian critical systems. In this work, we investigate the cMERA of non-Hermitian critical systems using a biorthogonal basis. Our findings indicate that the emergent spacetime corresponds to de Sitter (dS) spacetime, with the right and left ground states of non-Hermitian systems localized at the future and past boundaries ($\mathcal{I}^{\pm}$) of dS spacetime. Furthermore, a revised RT formula is derived within this dS/cMERA correspondence.