Confinement in a mixed-dimensional XXZ model

We present our latest results on a mixed-dimensional XXZ model where one-dimensional XXZ chains are coupled through a simple Ising interaction. Our study is motivated by the progress in cold atom experiments, where such models can be readily simulated. We study the ground state phase diagrams of the mixed-dimensional XXZ model at zero and non-zero magnetization by using DMRG calculations where long-distance correlations are easily accessible. In addition, we also consider finite temperature calculations of the mixed-dimensional model and quenching the system from ordered to disordered regime.

Furthermore, we study the mixed-dimensional spin model in the context of a Z₂ lattice gauge theory (LGT), which is known to exhibit confinement of dynamical charges. We find a mapping between the spin model and a Z₂ LGT by considering spinon excitations in the XXZ chains as hard-core bosons on a dual lattice. The mapping exhibits the so-called Gauss law, that can be used to connect particle pairs with Z₂ strings. Such string picture simplifies the notion of confinement in the pure Z₂ LGT. However, the resulting Z₂ LGT model explicitly breaks the U(1) charge conservation, which again complicates the study of confinement with the usual condensed matter techniques. As a result we propose to probe the confinement by considering histograms of Z₂ string and anti-string lengths, which we obtain from snapshots sampled from matrix product states. This is a tractable method to experimentally probe confinement since snapshots are readily available in cold atom experiments.