Everybody is welcome to attend the online QuSoft seminar with:
Tamara Kohler at 2 pm
title: Toy models of holographic duality between local Hamiltonians
abstract: 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. HQECC give a mapping of states and observables. However, they do not map local bulk Hamiltonians to local Hamiltonians on the boundary. In this talk I'll introduce a construction
where we combine 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. It also allows us to construct a map in the reverse direction: from local boundary Hamiltonians to the
corresponding local Hamiltonian in the bulk. Under this boundary-to-bulk mapping, the bulk geometry emerges as an approximate, low-energy, effective theory living in the code-space of an (approximate) HQECC on the boundary. At higher energy scales, this emergent bulk geometry is modified in a way that matches the toy models of black holes proposed
previously for HQECC. Moreover, the duality on the level of dynamics shows how these toy-model black holes can form dynamically.
Harriet Apel at 3 pm
title: Holographic duality between local Hamiltonians from random tensor networks
abstract: The AdS/CFT correspondence realises the holographic principle where information in the bulk of a space is encoded at its border. We are yet a long way from a full mathematical construction of AdS/CFT, but toy models in the form of holographic quantum error correcting codes (HQECC) have replicated some interesting features of the correspondence. In this work we construct new HQECCs built from random stabilizer
tensors that describe a duality between models encompassing local Hamiltonians whilst exactly obeying the Ryu-Takayanagi entropy formula for all boundary regions. We also obtain complementary recovery of local bulk operators for any boundary bipartition. Existing HQECCs have been shown to exhibit these properties individually, whereas our
mathematically rigorous toy models capture these features of AdS/CFT simultaneously, advancing further towards a complete construction of holographic duality.
For the link please contact Jop Briet or Suhasree Patro.
