Fermionic van Hemmen Spin Glass Model with a Transverse Field

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field $\Gamma$. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by $\Gamma$. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential $\mu$ and $\Gamma$. The $\Gamma$ field suppresses the magnetic orders. The increase of $\mu$ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by $\mu$. In addition, $\mu$ can change the nature of the phase boundaries introducing a first order transition.