We implement the coupled cluster method to very high orders of approximation to study the spin-$\frac{ 1}{ 2}$ $J_{ 1}$--$J_{ 2}$ 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 $J_{ 2} \equiv \alpha J_{ 1} > 0$. By studying the magnetic order parameter (i.e., the average local on-site magnetization) in the range $0 \leq \alpha \leq 1$ of the frustration parameter we find that the quasiclassical antiferromagnetic N\'{ e}el and (so-called) double N\'{ e}el states form the stable ground-state phases in the respective regions $\alpha < \alpha_{ 1a}^{ c} = 0.46(1)$ and $\alpha > \alpha_{ 1b}^{ c} = 0.615(5)$. The double N\'{ e}el state has N\'{ e}el ($\cdots\uparrow\downarrow\uparrow\downarrow\cdots$) ordering along the (column) direction parallel to the stripes of squares with both or no $J_{ 2}$ bonds, and spins alternating in a pairwise ($\cdots\uparrow\uparrow\downarrow\downarrow\uparrow\uparrow\downarrow\downarrow\cdots$) 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 $\alpha_{ 1a}^{ c} < \alpha < \alpha_{ 1b}^{ c}$ is a gapped state with no discernible long-range magnetic order.
Categories: cond-mat.str-el