Glassy dynamics from quark confinement: Atomic quantum simulation of the gauge-Higgs model on a lattice

In the previous works, we proposed atomic quantum simulations of the U(1) gauge-Higgs model by ultracold Bose gases. By studying extended Bose-Hubbard models (EBHMs) including long-range repulsions, we clarified the locations of the confinement, Coulomb, and Higgs phases. In this paper, we study the EBHM with nearest-neighbor repulsions in one and two dimensions at large fillings by the Gutzwiller variational method. We obtain phase diagrams and investigate dynamical behavior of electric flux from the gauge-theoretical point of view. We also study if the system exhibits glassy quantum dynamics in the absence and presence of quenched disorder. We explain that the obtained results have a natural interpretation in the gauge theory framework. Our results suggest important perspective on many-body localization in strongly correlated systems. They are also closely related to anomalously slow dynamics observed by recent experiments performed on the Rydberg atom chain, and our study indicates existence of similar phenomenon in two-dimensional space.