Construction of Entangled Many-body States via the Higgs Mechanism

We provide a guiding principle to generate entanglement of quantum many-body states by applying the Higgs mechanism to systems without gauge structures. A unitary operator associated with the Higgs mechanism is constructed, named as mean-operator, and employed to prepare an entangled many-body state out of a trivial state. We investigate symmetry-protected-topological states with two Ising symmetries. Plausible applications to quantum simulators such as Rydberg atoms and trapped ions, are also discussed, interpreting the mean-operators as the Ising coupling gates.