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Within the framework of the Kondo-Heisenberg model, we analyse the effect ofcharge fluctuation on the modulated spin liquid (MSL) and antiferromagnetic(AF) orders which were established in a previous publication. We discuss theemergence of two quantum critical lines separating the coexisting Kondo-MSL andKondo-MSL-AF phases. The various order parameters of the system possess acharacteristic signature observable on the electronic band structure of each ofthe phases. We calculate that the MSL order is indeed a possible explanation ofthe hidden order phase of $URu_{2}Si_{2}$ heavy fermion compound. Our modelproduces results in qualitative agreement with the experimental (T,P) phasediagram and the two gap openings in the system and quantitative agreement withthe entropy and Sommerfeld coefficient evolution.

Modulated Spin Liquid and Magnetic Order from a Kondo-Heisenberg model applied to $URu_{2}Si_{2}$