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We investigate the phase diagram of hard-core bosons on a square lattice withcompeting interactions. The hard-core bosons can be represented also byspin-1/2 operators and the model can therefore be mapped onto an anisotropic$J_1$-$J_2$-Heisenberg model. We find the N\'eel state and a collinearantiferromagnetic state as classical ordered phases to be suppressed for smallferromagnetic exchange terms $J_{1,2}^{x,y}$ and a ferromagnetic phase whichorders in the x-y-plane for large $J_{1,2}^{x,y}$. For an intermediate regimethe emergence of new quantum states like valence bond crystals or super-solidsis predicted for similar models. We do not observe any signal for long-rangeorder in terms of conventional order or dimer correlations in our model andfind an exponential decay in the spin correlations. Hence, all evidence ispointing towards a quantum disordered ground state for a small region in thephase diagram.

Quantum disordered ground state for hard-core bosons on the frustrated square lattice