Constraint-based scheme for realizing Z2 lattice gauge theories with matter in (2+1)-D

Lattice gauge theories (LGTs) coupled to matter have been out of reach of table-top experiments for decades. Recent developments in the field, in particular of Rydberg atom arrays and superconducting qubits (SCQs), have moved this goal within reach for state-of-the-art analog quantum simulation platforms and NISQ devices. In this talk, I will propose an elegant and readily realizable scheme to experimentally simulate Z2 LGTs coupled to matter in (1+1) and (2+1)-dimensions suitable for Rydberg atom arrays or SCQs. The scheme is based on a novel protection scheme using local pseudo generators (LPGs) to stabilize a target gauge sector. The proposal allows to study many topics of Z2 LGTs in the strong coupling limit that are currently extremely challenging to address numerically in (2+1)-D. The list of topics include the presence of an exotic topological, deconfined (Toric Code) phase, the details of a deconfinement-confinement transition or the Schwinger effect, to name a few. Starting from a microscopic Hamiltonian in the lab frame, I will derive an effective Hamiltonian that describes a Z2 LGTs coupled to matter, and compare to large-scale numerical simulations.