Studying 2D Lattice Gauge Theories with Tensor Networks

For years Tensor Networks have been exploited to study many-body-physics problems mostly in the field of Condensed Matter Physics. Its application to Lattice Gauge Theories is a much newer field. I will review the motivation behind using Tensor Networks for Lattice Gauge Theories and introduce the state-of-the-art problems that are being tackled. The remainder of the talk will consist in showing how a particular type of Tensor Network called Infinite Projected Entangled Pair States (iPEPS) can be used to simulate a 2+1d Z_3 lattice gauge theory. This represents a crucial step towards attempting simulations of more challenging gauge groups and higher dimensions.