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 be represented also by spin-1/2 operators and the model can therefore be mapped onto an anisotropic $J_1$-$J_2$-Heisenberg model. We find the Néel state and a collinear antiferromagnetic state as classical ordered phases to be suppressed for small ferromagnetic exchange terms $J_{1,2}^{x,y}$ and a ferromagnetic phase which orders in the x-y-plane for large $J_{1,2}^{x,y}$. For an intermediate regime the emergence of new quantum states like valence bond crystals or super-solids 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 towards a quantum disordered ground state for a small region in the phase diagram.

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