A holographic duality from lifted tensor networks

Tensor networks provide an efficient classical representation of certain strongly correlated quantum many-body systems. We present a general lifting method to ascribe quantum states to the network structure itself that reveals important new physical features. To illustrate, we focus on the multiscal...

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Bibliographic Details
Published in:npj quantum information 2020-04, Vol.6 (1), Article 36
Main Authors: McMahon, Nathan A., Singh, Sukhbinder, Brennen, Gavin K.
Format: Article
Language:English
Subjects:
639/766/483/481
639/766/483/640
Classical and Quantum Gravitation
Physics
Physics and Astronomy
Quantum Computing
Quantum Field Theories
Quantum Information Technology
Quantum Physics
Relativity Theory
Spintronics
String Theory
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Summary:Tensor networks provide an efficient classical representation of certain strongly correlated quantum many-body systems. We present a general lifting method to ascribe quantum states to the network structure itself that reveals important new physical features. To illustrate, we focus on the multiscale entanglement renormalization ansatz (MERA) tensor network for 1D critical ground states on a lattice. The MERA representation of the said state can be lifted to a 2D quantum dual in a way that is suggestive of a lattice version of the holographic correspondence from string theory. The bulk 2D state has an efficient quantum circuit construction and exhibits several features of holography, including the appearance of horizon-like holographic screens, short-ranged correlations described via a strange correlator and bulk gauging of global on-site symmetries at the boundary. Notably, the lifting provides a way to calculate a quantum-corrected Ryu–Takayanagi formula, and map bulk operators to boundary operators and vice versa.
ISSN:2056-6387
2056-6387
DOI:10.1038/s41534-020-0255-7