We study the relationship between the zeros of the Riemann zeta function and physical systems exhibiting supersymmetry, PT symmetry and SU(2) group symmetry. Our findings demonstrate that unbroken supersymmetry is associated with the presence of non-trivial zeros of the zeta function. However for other cases supersymmetry is spontaneously broken and the ground state energy of the system is not zero. Moreover, we have established the manifestation of PT symmetry invariance within our supersymmetric 
system. In addition, our findings provide insights into a SU(2) symmetry that arises within these systems, with the Hilbert space having two level structure.