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

Abstract We implement the coupled cluster method to very high orders of approximation to study the spin- 1 2 J 1 – J 2 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 J 1 > 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 J 2 ≡ α J 1 > 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 Neel and (so-called) double Neel states form the stable ground-state phases in the respective regions α α 1 a c = 0 . 46 ( 1 ) and α > α 1 b c = 0.615 ( 5 ) . The double Neel state has Neel ( ⋯ ↑ ↓ ↑ ↓ ⋯ ) ordering along the (column) direction parallel to the stripes of squares with both or no J 2 bonds, and spins alternating in a pairwise ( ⋯ ↑ ↑ ↓ ↓ ↑ ↑ ↓ ↓ ⋯ ) fashion along the perpendicular (row) direction, so that the parallel pairs occur on squares with both J 2 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 1 a c α α 1 b c is a gapped state with no discernible long-range magnetic order.