  Recently, the possibility of quantum simulation of dynamical gauge fields was
pointed out by using a system of cold atoms trapped on each link in an optical
lattice. However, to implement exact local gauge invariance, fine-tuning the
interaction parameters among atoms is necessary. In the present paper, we study
the effect of violation of the U(1) local gauge invariance by relaxing the
fine-tuning of the parameters and showing that a wide variety of cold atoms is
still to be a faithful quantum simulator for a U(1) gauge-Higgs model
containing a Higgs field sitting on sites. Clarification of the dynamics of
this gauge-Higgs model sheds some lights upon various unsolved problems
including the inflation process of the early universe. We study the phase
structure of this model by Monte Carlo simulation, and also discuss the atomic
characteristics of the Higgs phase in each simulator.
