Conference

In this talk I will give an overview of tensor network approaches to critical systems. I will discuss entanglement scaling laws, show how PEPS can simulate systems with Fermi surfaces, and present some results for simulating systems in the continuum.

The suitability of tensor network ansatzes for the description of physically relevant states in one dimensional lattice gauge theories (LGT) has been demonstrated in the last years by a large amount of systematic studies, including abelian and non-abelian LGTs, and including scenarios where traditional Monte Carlo approaches fail due to a sign problem. While this establishes a solid motivation to extend the program to higher dimensions, a similar systematic study in two dimensions using PEPS requires dealing with specific considerations. Besides a larger computational costs associated to the higher spatial dimension, the presence of plaquette terms in LGTs hinders the efficiency of the most up-to-date PEPS algorithms. With a newly developed update strategy, nevertheless, such terms can be treated by the most efficient techniques. We have used this method to perform the first ab initio iPEPS study of a LGT in 2+1 dimensions: a Z3 invariant model, for which we have determined the phase diagram.