Analog quantum simulation of (1+1)-dimensional lattice QED with trapped ions

nite-size scaling, we demonstrate that this model recovers Wilson’s lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge elds by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting smallscale implementations in a linear Paul trap. Both schemes work on energy scales signicantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman’s quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.