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

We investigate the phase diagram of hard-core bosons on a square lattice with competing interactions. The hard-core bosons can also be represented by spin-1/2 operators and the model can therefore be mapped onto an anisotropic J₁-J₂ Heisenberg model. We find the Néel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed by the introduction of ferromagnetic exchange terms in the x-y plane that result in a ferromagnetic phase for large interactions. For an intermediate regime, the emergence of new quantum states like valence bond crystals or supersolids is predicted for similar models. We do not observe any signal for long-range order in terms of conventional order or dimer correlations in our model and find an exponential decay in the spin correlations. Hence, all evidence is pointing toward a quantum-disordered ground state for a small region in the phase diagram.