Holographic Spin Networks from Tensor Network States

Tensor networks are a powerful tool for describing many body systems, they reduce the complexity of storing and computing many-body states by restricting the state space to have a restricted entanglement structure. The multiscale entanglement renormalization ansatz (MERA) is one such example of tensor network state designed to approximate many body states with conformal symmetries (i.e. spin chains). For 1D periodic states the MERA can be visualized as a disc where the quantum state is on the boundary and the tensor network is embedded into the bulk of the disc, reminiscent of the holographic principle where theories of quantum gravity are expected to be encodable onto the system's boundary.

In this presentation I will discuss a toy model we have developed, focusing on the MERA but extendible to any tensor network state, motivated by the holographic principle. Adding degrees of freedom into the bulk of the network we discuss relationships between properties of the boundary and the bulk of the tensor network with a motivation towards adapting tools from the holographic principle for use in strongly correlated many-body systems. To do this we compute correlation functions, Wilson loops, and entropic quantities in the bulk for a number of critical spin chains with on-site symmetries.