Holographic toy models with matchgate tensor networks

Abstract: Much insight into the quantum information side of holographic dualities has come from studying simple toy models based on tensor networks. While these models have been shown to realize properties such as entanglement and quantum error correction in line with continuum AdS/CFT, their boundary states differ from those of simple lattice discretizations of CFTs. In this talk, I will introduce a class of tensor networks based on matchgate tensors for which such toy models can be efficiently constructed. Within this class, we will find simple solutions that are identified with a local, critical boundary Hamiltonian corresponding to a disordered version of the critical Ising model. Rather than just ground states, we will find that the matchgate tensor ansatz can also reproduce low-energy excited states of the boundary Hamiltonian, leading to a concrete bulk-boundary dictionary between bulk and boundary states. I will argue that this can be extended to a new class of holographic codes related to imaginary-time path integrals, which serves as a promising avenue to study time dynamics in holographic tensor network models.

HEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

Purdue HET

Series comments: The recorded talks will be available on YouTube here: www.youtube.com/playlist?list=PLxU3vHZccQj64m9zsQR74D5WP1z1g4t1J