Construction of entangled many-body states via the Higgs mechanism

Abstract

We provide a guideline to generate entanglement of quantum many-body states by applying key ideas of the Higgs mechanism to systems without gauge structures. By demoting a Z2 gauge structure, the model with the global Z2 X Z2 symmetry is constructed on a square lattice. We show that its ground state is a symmetry-protected-topological state protected by the global Z2 X Z2 symmetry and translational symmetry, in contrast to the previous work where one-form symmetry is introduced for protection. Furthermore, by demoting a U (1) gauge structure, an intriguing gapless state with the global U (1) X Z is constructed. We discuss the generalization of our model to different symmetries and lattices. Plausible applications to quantum simulators, such as Rydberg atoms and trapped ions, are also discussed.