Synthetic U(1) gauge invariance in a spin-1 Bose gas

Recent experimental realizations of the U(1) gauge invariance [Nature (London) 587, 392 (2020)10.1038/s41586-020-2910-8; Science 367, 1128 (2020)10.1126/science.aaz5312] open a door for quantum simulation of elementary particles and their interactions using ultracold atoms. Stimulated by such exciting progress, we propose a platform—a spin-1 Bose-Einstein condensate—to simulate the deconfined lattice Schwinger model. Unlike previous platforms, it is shown that the atomic interactions in the spin-1 condensate naturally lead to a matter-field interaction term which respects the U(1) gauge symmetry. As a result, a new Z_{3}-ordered phase with threefold ground-state degeneracy emerges in the phase diagram. The Z_{3} phase connects to the disordered phase by a three-state Potts criticality, which is in contrast to the conventional Coleman's transition with Ising criticality. Furthermore, the ordered state is constructed by a set of weak quantum scars, which is responsible for the anomalously slow dynamics as it is quenched to a special point in the phase diagram. Our proposal provides a platform for extracting emergent physics in synthetic gauge systems with matter-field interactions.