Gapped paramagnetic state in a frustrated spin-½ Heisenberg antiferromagnet on the cross-striped square lattice

We implement the coupled cluster method to very high orders of approximation to study the spin-½ J₁-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 ≡ α J₁ > 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 < α^c_1a = 0:46(1) and α > α^c_1b = 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 α^c_1a < α < α^c_1b is a gapped state with no discernible long-range magnetic order.