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

TL;DR

This review discusses recent theoretical advances in tensor network states, focusing on symmetries, fermions, entanglement, and their connections to holography, highlighting the role of entanglement in physical properties.

Contribution

It summarizes recent developments in tensor network theory, emphasizing the integration of symmetries, fermionic systems, entanglement calculations, and holographic dualities.

Findings

Enhanced understanding of symmetry effects in TN states

Development of fermionic tensor network methods

Insights into entanglement Hamiltonians and holography

Abstract

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.