Confinement of Z₂ lattice gauge theories in a mixed-dimensional XXZ model

The study of confinement in lattice gauge theories (LGTs) is one of the fundamental problems in physics, which is still poorly understood when gauge fields are coupled to dynamical matter. In this talk we explore the physics of confinement in a mixed-dimensional XXZ model, where XXZ chains are coupled by an Ising interaction. We map this system to coupled arrays of Z₂ LGTs, where Z₂ charges correspond to spinons in the spin picture. Using numerical simulations we uncover stripes in the ground state, which can be melted into a disordered deconfined state by increasing the hopping amplitude of the Z₂ charges. In addition, finite temperature calculations reveal an intricate gas of confined mesons, which emerges as a result of stripes being destroyed by thermal fluctuations and the development of long-range AFM correlations in the spin picture. In the Z₂ LGT picture this results in a finite electric field that confines parton pairs into bound mesons. Our study is motivated by the quantum simulation of a Bose-Hubbard Hamiltonian with dipolar atoms, which can be effectively mapped to the coupled arrays of Z₂ LGT and the mixed-dimensional XXZ model in the hardcore limit when hopping is limited to one dimension. By quantum simulation of the full Bose-Hubbard model we experimentally realize a transition between stripes and deconfined state, and demonstrate that such platform can be used to study confinement of a Z₂ lattice gauge theory.