Tensor Network Toy Models of Holographic Dualities: Locality and Causality
7Tamara Kohler (Stanford University)
https://simons.berkeley.edu/talks/tamara-kohler-stanford-university-2024-03-21
Quantum Complexity: Quantum PCP, Area Laws, and Quantum Gravity
Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. The original HQECC gave a mapping of states and observables. However, they did not map local bulk Hamiltonians to local Hamiltonians on the boundary, and did not preserve causal features of the duality. In this talk I will present work combining HQECC with Hamiltonian simulation theory to construct a bulk-boundary mapping between local Hamiltonians, whilst retaining all the features of the HQECC duality. This allows us to construct a duality between models, encompassing the relationship between bulk and boundary energy scales and time dynamics. I will also discuss a modification to these models which introduces some of the expected causal properties of AdS/CFT into the toy models, and outline what features of the duality are still missing from these toy models.