Tensor network simulation of QED on infinite lattices: learning from (1+1)d, and prospects for (2+1)d

Understand

The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful.

• The vision is that such methods will, eventually, be used to simulate theories in $(3+1)$ dimensions in regimes difficult for other methods.
• So far, however, TN methods have mostly simulated lattice gauge theories in $(1+1)$ dimensions.
• The aim of this paper is to explore the simulation of quantum electrodynamics (QED) on infinite lattices with TNs, i.e., fermionic matter fields coupled to a $U(1)$ gauge field, directly in the thermodynamic limit.