Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography

Understand

This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems.

• Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement Hamiltonians from Projected Entangled Pair States (PEPS), and the relation between the Multi-scale Entanglement Renormalization Ansatz (MERA) and the AdS/CFT or gauge/gravity duality.
• We stress the role played by entanglement in the emergence of several physical properties and objects through the TN language.
• Some recent results along these lines are also discussed.