Gapped paramagnetic state in a frustrated spin-12 Heisenberg antiferromagnet on the cross-striped square lattice

We implement the coupled cluster method to very high orders of approximation to study the spin-12J1-J2 Heisenberg model on a cross-striped square lattice. Every nearest-neighbour pair of sites on the square lattice has an isotropic antiferromagnetic exchange bond of strength J1>0, while the basic square plaquettes in alternate columns have either both or neither next-nearest-neighbour (diagonal) pairs of sites connected by an equivalent frustrating bond of strength J2≡αJ1>0. By studying the magnetic order parameter (i.e., the average local on-site magnetization) in the range 0≤α≤1 of the frustration parameter we find that the quasiclassical antiferromagnetic Néel and (so-called) double Néel states form the stable ground-state phases in the respective regions α<α1ac=0.46(1) and α>α1bc=0.615(5). The double Néel state has Néel (⋯↑↓↑↓⋯) ordering along the (column) direction parallel to the stripes of squares with both or no J2 bonds, and spins alternating in a pairwise (⋯↑↑↓↓↑↑↓↓⋯) fashion along the perpendicular (row) direction, so that the parallel pairs occur on squares with both J2 bonds present. Further explicit calculations of both the triplet spin gap and the zero-field uniform transverse magnetic susceptibility provide compelling evidence that the ground-state phase over all or most of the intermediate regime α1ac<α<α1bc is a gapped state with no discernible long-range magnetic order.