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Recently, the possibility of quantum simulation of dynamical gauge fields waspointed out by using a system of cold atoms trapped on each link in an opticallattice. However, to implement exact local gauge invariance, fine-tuning theinteraction parameters among atoms is necessary. In the present paper, we studythe effect of violation of the U(1) local gauge invariance by relaxing thefine-tuning of the parameters and showing that a wide variety of cold atoms isstill to be a faithful quantum simulator for a U(1) gauge-Higgs modelcontaining a Higgs field sitting on sites. Clarification of the dynamics ofthis gauge-Higgs model sheds some lights upon various unsolved problemsincluding the inflation process of the early universe. We study the phasestructure of this model by Monte Carlo simulation, and also discuss the atomiccharacteristics of the Higgs phase in each simulator.

Atomic Quantum Simulation of Lattice Gauge-Higgs Model: Higgs Couplings and Emergence of Exact Local Gauge Symmetry