  We provide a guiding principle to generate entanglement of quantum many-body
states by applying key ideas of the Higgs mechanism to systems without gauge
structures. Unitary operators associated with the Higgs mechanism are
constructed, named as mean-operators, and employed to prepare entangled
many-body states out of a trivial state. We uncover a
symmetry-protectedtopological state with two Ising symmetries on a square
lattice and find entangled states with different symmetries and lattices.
Plausible applications to quantum simulators such as Rydberg atoms and trapped
ions, are also discussed, interpreting the mean-operators as the Ising coupling
gates.
