We study the interplay of superfluidity, glassy, and magnetic orders in the $XXZ$ model with random Ising interactions on a three dimensional cubic lattice. In the classical limit, this model reduces to a $\pm J$ Edwards-Anderson Ising model with concentration $p$ of ferromagnetic bonds, which hosts a glassy-ferromagnetic transition at a critical concentration $p_c^{\mathrm{cl}}\sim 0.77$. Our quantum Monte Carlo simulation results show that quantum fluctuations stabilize the coexistence of superfluidity and glassy order (superglass), and shift the (super)glassy-ferromagnetic transition to $p_c>p_c^{\mathrm{cl}}$. In contrast, antiferromagnetic order coexists with superfluidity to form a supersolid, and the transition to the glassy phase occurs at a higher $p$.

• Received 14 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.157202